title: Roh Tae-woo

text: The "trial of the century", as described by the media, saw both convicted in August 1996 for treason, mutiny, and corruption; Chun was sentenced to death, later commuted to life imprisonment, while Roh's 22½-year jail sentence was reduced to 17 years on appeal. Both were released from prison in December 1997 and pardoned by Kim Young-sam on advice of president-elect Kim Dae-jung. Both Roh and Chun attended Kim Dae-jung's inauguration on 25 February 1998.


title: Roh Tae-woo

text: Roh finished repaying fines from his illegally gained wealth in 2013. In 2013, the remaining W24 billion (USD22 million) of a W262.9 billion fine for corruption in office was paid. He mostly stayed out of politics and maintained a low profile in retirement, and he continued to express remorse over his crimes until his death in 2021. In 2019, two years before Roh's death, his son went to Gwangju and visited the May 18th National Cemetery on behalf of his father. Roh's son visited the cemetery a second time in 2020, and he offered a flower wreath under his father's name. In contrast, his friend and predecessor, Chun Doo-hwan stopped repaying his remaining fine and did not show regret or remorse for his past actions.


title: Roh Tae-woo

text: Roh suffered from prostate cancer and received surgery in 2002. He also suffered from cerebellar atrophy and asthma. His son, Roh Jae-heon who is a lawyer based in the United States, said that Roh spent most of his final 10 years of his life in the hospital, while his daughter Roh Soh-yeong, an art museum director, said he was bedridden for the past 10 years and unable to speak or move his body.


title: Roh Tae-woo

text: Roh died in intensive care at the Seoul National University Hospital at 1:45pm KST on 26 October 2021, at the age of 88. Roh's family released his last will and message, asking for forgiveness for his role in the 1979 military coup and 1980 Gwangju Uprising crackdown, and expressed his wish for future generations to be able to achieve reunification with North Korea which he could not achieve in his term.


title: Roh Tae-woo

text: In view of Roh's mixed and disputed legacy, the government decided to hold a state funeral for Roh following a debate within the national cabinet, in recognition of his "significant contributions to the nation's development". The decision was criticized by some, including survivors and victims' families of the Gwangju crackdown and members of the ruling liberal Democratic Party. The city of Gwangju and several other cities and provincial governments refused to raise flags half-mast or set up memorial altars for Roh in accordance with state funeral procedures. In Seoul, memorial altars saw a low turnout of mourners coming to pay their respects.


title: Roh Tae-woo

text: The scaled-down state funeral service, held in the middle of the COVID-19 pandemic, took place at Olympic Park, Seoul on 30 October, in recognition of the 1988 Summer Olympics which was successfully held there under his presidency. Prime Minister Kim Boo-kyum gave a eulogy. By law, Roh was not eligible for burial at a national cemetery because of his past criminal record and conviction. He was cremated and his ashes were interred at Unification Hill at Paju, a border town to North Korea.


title: Roh Tae-woo

text: He died about one month before former President Chun Doo-hwan died on 23 November 2021 from complications of blood cancer.


title: Railway track

text: A railway track (British English and UIC terminology) or railroad track (American English), also known as permanent way or simply track, is the structure on a railway or railroad consisting of the rails, fasteners, railroad ties (sleepers, British English) and ballast (or slab track), plus the underlying subgrade. It enables trains to move by providing a dependable surface for their wheels to roll upon. Early tracks were constructed with wooden or cast iron rails, and wooden or stone sleepers; since the 1870s, rails have almost universally been made from steel.


title: Railway track

text: The first railway in Britain was the Wollaton Wagonway, built in 1603 between Wollaton and Strelley in Nottinghamshire. It used wooden rails and was the first of around 50 wooden-railed tramways built over the next 164 years. These early wooden tramways typically used rails of oak or beech, attached to wooden sleepers with iron or wooden nails. Gravel or small stones were packed around the sleepers to hold them in place and provide a walkway for the people or horses that moved wagons along the track. The rails were usually about long and were not joined - instead, adjacent rails were laid on a common sleeper. The straight rails could be angled at these joints to form primitive curved track.


title: Railway track

text: When steam locomotives were introduced, starting in 1804, the track then in use proved too weak to carry the additional weight. Richard Trevithick's pioneering locomotive at Pen-y-darren broke the plateway track and had to be withdrawn. As locomotives became more widespread in the 1810s and 1820s, engineers built rigid track formations, with iron rails mounted on stone sleepers, and cast-iron chairs holding them in place. This proved to be a mistake, and was soon replaced with flexible track structures that allowed a degree of elastic movement as trains passed over them.


title: Railway track

text: Traditionally, tracks are constructed using flat-bottomed steel rails laid on and spiked or screwed into timber or pre-stressed concrete sleepers (known as ties in North America), with crushed stone ballast placed beneath and around the sleepers.


title: Railway track

text: Most modern railroads with heavy traffic use continuously welded rails that are attached to the sleepers with base plates that spread the load. When concrete sleepers are used, a plastic or rubber pad is usually placed between the rail and the tie plate. Rail is usually attached to the sleeper with resilient fastenings, although cut spikes are widely used in North America. For much of the 20th century, rail track used softwood timber sleepers and jointed rails, and a considerable amount of this track remains on secondary and tertiary routes.


title: Railway track

text: In North America and Australia, flat-bottomed rails were typically fastened to the sleepers with dog spikes through a flat tie plate. In Britain and Ireland, bullhead rails were carried in cast-iron chairs which were spiked to the sleepers. In 1936, the London, Midland and Scottish Railway pioneered the conversion to flat-bottomed rail in Britain, though earlier lines had made some use of it.


title: Railway track

text: Jointed rails were used at first because contemporary technology did not offer any alternative. However, the intrinsic weakness in resisting vertical loading results in the ballast becoming depressed and a heavy maintenance workload is imposed to prevent unacceptable geometrical defects at the joints. The joints also needed to be lubricated, and wear at the fishplate (joint bar) mating surfaces needed to be rectified by shimming. For this reason jointed track is not financially appropriate for heavily operated railroads.


title: Railway track

text: Timber sleepers are of many available timbers, and are often treated with creosote, chromated copper arsenate, or other wood preservatives. Pre-stressed concrete sleepers are often used where timber is scarce and where tonnage or speeds are high. Steel is used in some applications.


title: Railway track

text: The track ballast is customarily crushed stone, and the purpose of this is to support the sleepers and allow some adjustment of their position, while allowing free drainage.


title: Railway track

text: A disadvantage of traditional track structures is the heavy demand for maintenance, particularly surfacing (tamping) and lining to restore the desired track geometry and smoothness of vehicle running. Weakness of the subgrade and drainage deficiencies also lead to heavy maintenance costs. This can be overcome by using ballastless track. In its simplest form this consists of a continuous slab of concrete (like a highway structure) with the rails supported directly on its upper surface (using a resilient pad).


title: Railway track

text: There are a number of proprietary systems; variations include a continuous reinforced concrete slab and the use of pre-cast pre-stressed concrete units laid on a base layer. Many permutations of design have been put forward.


title: Railway track

text: However, ballastless track has a high initial cost, and in the case of existing railroads the upgrade to such requires closure of the route for a long period. Its whole-life cost can be lower because of the reduction in maintenance. Ballastless track is usually considered for new very high speed or very high loading routes, in short extensions that require additional strength (e.g. railway stations), or for localised replacement where there are exceptional maintenance difficulties, for example in tunnels. Most rapid transit lines and rubber-tyred metro systems use ballastless track.


title: Railway track

text: Early railways (c. 1840s) experimented with "continuous bearing" railtrack, in which the rail was supported along its length, with examples including Brunel's baulk road on the Great Western Railway, as well as use on the Newcastle and North Shields Railway, on the Lancashire and Yorkshire Railway to a design by John Hawkshaw, and elsewhere. Continuous-bearing designs were also promoted by other engineers. The system was tested on the Baltimore and Ohio railway in the 1840s, but was found to be more expensive to maintain than rail with cross sleepers.


title: Railway track

text: This type of track still exists on some bridges on Network Rail where the timber baulks are called waybeams or longitudinal timbers. Generally the speed over such structures is low.


title: Railway track

text: Later applications of continuously supported track include Balfour Beatty's 'embedded slab track', which uses a rounded rectangular rail profile (BB14072) embedded in a slipformed (or pre-cast) concrete base (development 2000s). The 'embedded rail structure', used in the Netherlands since 1976, initially used a conventional UIC 54 rail embedded in concrete, and later developed (late 1990s) to use a 'mushroom' shaped SA42 rail profile; a version for light rail using a rail supported in an asphalt concrete–filled steel trough has also been developed (2002).


title: Railway track

text: Modern ladder track can be considered a development of baulk road. Ladder track utilizes sleepers aligned along the same direction as the rails with rung-like gauge restraining cross members. Both ballasted and ballastless types exist.


title: Railway track

text: Modern track typically uses hot-rolled steel with a profile of an asymmetrical rounded I-beam. Unlike some other uses of iron and steel, railway rails are subject to very high stresses and have to be made of very high-quality steel alloy. It took many decades to improve the quality of the materials, including the change from iron to steel. The stronger the rails and the rest of the trackwork, the heavier and faster the trains the track can carry.


title: Railway track

text: Other profiles of rail include: bullhead rail; grooved rail; flat-bottomed rail (Vignoles rail or flanged T-rail); bridge rail (inverted U–shaped used in baulk road); and Barlow rail (inverted V).


title: Railway track

text: North American railroads until the mid- to late-20th century used rails long so they could be carried in gondola cars (open wagons), often long; as gondola sizes increased, so did rail lengths.


title: Railway track

text: According to the "Railway Gazette International" the planned-but-cancelled 150-kilometre rail line for the Baffinland Iron Mine, on Baffin Island, would have used older carbon steel alloys for its rails, instead of more modern, higher performance alloys, because modern alloy rails can become brittle at very low temperatures.


title: Railway track

text: Early North American railroads used iron on top of wooden rails as an economy measure but gave up this method of construction after the iron came loose, began to curl, and intruded into the floors of the coaches. The iron strap rail coming through the floors of the coaches came to be referred to as "snake heads" by early railroaders.


title: Railway track

text: The Deeside Tramway in North Wales used this form of rail. It opened around 1870 and closed in 1947, with long sections still using these rails. It was one of the last uses of iron-topped wooden rails.


title: Railway track

text: Rail is graded by weight over a standard length. Heavier rail can support greater axle loads and higher train speeds without sustaining damage than lighter rail, but at a greater cost. In North America and the United Kingdom, rail is graded by its linear density in pounds per yard (usually shown as "pound" or "lb"), so "130-pound rail" would weigh . The usual range is . In Europe, rail is graded in kilograms per metre and the usual range is . The heaviest rail mass-produced was and was rolled for the Pennsylvania Railroad. The United Kingdom is in the process of transition from the imperial to metric rating of rail.


title: Railway track

text: The rails used in rail transport are produced in sections of fixed length. Rail lengths are made as long as possible, as the joints between rails are a source of weakness. Throughout the history of rail production, lengths have increased as manufacturing processes have improved.


title: Railway track

text: The following are lengths of single sections produced by steel mills, without any thermite welding. Shorter rails may be welded with flashbutt welding, but the following rail lengths are unwelded.


title: Railway track

text: Welding of rails into longer lengths was first introduced around 1893, making train rides quieter and safer. With the introduction of thermite welding after 1899, the process became less labour-intensive, and ubiquitous.


title: Railway track

text: Newer longer rails tend to be made as simple multiples of older shorter rails, so that old rails can be replaced without cutting. Some cutting would be needed as slightly longer rails are needed on the outside of sharp curves compared to the rails on the inside.


title: Railway track

text: Rails can be supplied pre-drilled with boltholes for fishplates or without where they will be welded into place. There are usually two or three boltholes at each end.


title: Railway track

text: Rails are produced in fixed lengths and need to be joined end-to-end to make a continuous surface on which trains may run. The traditional method of joining the rails is to bolt them together using metal fishplates (jointbars in the US), producing "jointed track". For more modern usage, particularly where higher speeds are required, the lengths of rail may be welded together to form "continuous welded rail" (CWR).


title: Railway track

text: Jointed track is made using lengths of rail, usually around long (in the UK) and long (in North America), bolted together using perforated steel plates known as "fishplates" (UK) or "joint bars" (North America).


title: Railway track

text: Fishplates are usually long, used in pairs either side of the rail ends and bolted together (usually four, but sometimes six bolts per joint). The bolts have alternating orientations so that in the event of a derailment and a wheel flange striking the joint, only some of the bolts will be sheared, reducing the likelihood of the rails misaligning with each other and exacerbating the derailment. This technique is not applied universally; European practice being to have all the bolt heads on the same side of the rail.


title: Railway track

text: Small gaps which function as expansion joints are deliberately left between the rail ends to allow for expansion of the rails in hot weather. European practice was to have the rail joints on both rails adjacent to each other, while North American practice is to stagger them. Because of these small gaps, when trains pass over jointed tracks they make a "clickety-clack" sound. Unless it is well-maintained, jointed track does not have the ride quality of welded rail and is less desirable for high speed trains. However, jointed track is still used in many countries on lower speed lines and sidings, and is used extensively in poorer countries due to the lower construction cost and the simpler equipment required for its installation and maintenance.


title: Railway track

text: A major problem of jointed track is cracking around the bolt holes, which can lead to breaking of the rail head (the running surface). This was the cause of the Hither Green rail crash which caused British Railways to begin converting much of its track to continuous welded rail.


title: Railway track

text: Where track circuits exist for signalling purposes, insulated block joints are required. These compound the weaknesses of ordinary joints. Specially-made glued joints, where all the gaps are filled with epoxy resin, increase the strength again.


title: Railway track

text: As an alternative to the insulated joint, audio frequency track circuits can be employed using a tuned loop formed in approximately of the rail as part of the blocking circuit. Some insulated joints are unavoidable within turnouts.


title: Railway track

text: Another alternative is an axle counter, which can reduce the number of track circuits and thus the number of insulated rail joints required.


title: Railway track

text: Most modern railways use "continuous welded rail" (CWR), sometimes referred to as "ribbon rails". In this form of track, the rails are welded together by utilising flash butt welding to form one continuous rail that may be several kilometres long. Because there are few joints, this form of track is very strong, gives a smooth ride, and needs less maintenance; trains can travel on it at higher speeds and with less friction. Welded rails are more expensive to lay than jointed tracks, but have much lower maintenance costs. The first welded track was used in Germany in 1924. and has become common on main lines since the 1950s.


title: Railway track

text: The preferred process of flash butt welding involves an automated track-laying machine running a strong electric current through the touching ends of two unjoined rails. The ends become white hot due to electrical resistance and are then pressed together forming a strong weld. Thermite welding is used to repair or splice together existing CWR segments. This is a manual process requiring a reaction crucible and form to contain the molten iron.


title: Railway track

text: North American practice is to weld segments of rail at a rail facility and load it on a special train to carry it to the job site. This train is designed to carry many segments of rail which are placed so they can slide off their racks to the rear of the train and be attached to the ties (sleepers) in a continuous operation.


title: Railway track

text: If not restrained, rails would lengthen in hot weather and shrink in cold weather. To provide this restraint, the rail is prevented from moving in relation to the sleeper by use of clips or anchors. Attention needs to be paid to compacting the ballast effectively, including under, between, and at the ends of the sleepers, to prevent the sleepers from moving. Anchors are more common for wooden sleepers, whereas most concrete or steel sleepers are fastened to the rail by special clips that resist longitudinal movement of the rail. There is no theoretical limit to how long a welded rail can be. However, if longitudinal and lateral restraint are insufficient, the track could become distorted in hot weather and cause a derailment. Distortion due to heat expansion is known in North America as sun kink, and elsewhere as buckling. In extreme hot weather special inspections are required to monitor sections of track known to be problematic. In North American practice, extreme temperature conditions will trigger slow orders to allow for crews to react to buckling or "sun kinks" if encountered. The German railway company Deutsche Bahn is starting to paint rails white to lower the peak temperatures reached in summer days.


title: Railway track

text: After new segments of rail are laid, or defective rails replaced (welded-in), the rails can be artificially stressed if the temperature of the rail during laying is cooler than what is desired. The stressing process involves either heating the rails, causing them to expand, or stretching the rails with hydraulic equipment. They are then fastened (clipped) to the sleepers in their expanded form. This process ensures that the rail will not expand much further in subsequent hot weather. In cold weather the rails try to contract, but because they are firmly fastened, cannot do so. In effect, stressed rails are a bit like a piece of stretched elastic firmly fastened down. In extremely cold weather, rails are heated to prevent "pull aparts".


title: Railway track

text: CWR is laid (including fastening) at a temperature roughly midway between the extremes experienced at that location. (This is known as the "rail neutral temperature".) This installation procedure is intended to prevent tracks from buckling in summer heat or pulling apart in the winter cold. In North America, because broken rails are typically detected by interruption of the current in the signaling system, they are seen as less of a potential hazard than undetected heat kinks.


title: Railway track

text: Joints are used in the continuous welded rail when necessary, usually for signal circuit gaps. Instead of a joint that passes straight across the rail, the two rail ends are sometimes cut at an angle to give a smoother transition. In extreme cases, such as at the end of long bridges, a breather switch (referred to in North America and Britain as an "expansion joint") gives a smooth path for the wheels while allowing the end of one rail to expand relative to the next rail.


title: Railway track

text: A sleeper (tie) is a rectangular object on which the rails are supported and fixed. The sleeper has two main roles: to transfer the loads from the rails to the track ballast and the ground underneath, and to hold the rails to the correct width apart (to maintain the rail gauge). They are generally laid transversely to the rails.


title: Railway track

text: Various methods exist for fixing the rail to the sleeper. Historically spikes gave way to cast iron chairs fixed to the sleeper, more recently springs (such as "Pandrol clips") are used to fix the rail to the sleeper chair.


title: Railway track

text: Sometimes rail tracks are designed to be portable and moved from one place to another as required. During construction of the Panama Canal, tracks were moved around excavation works. These track gauge were and the rolling stock full size. Portable tracks have often been used in open pit mines. In 1880 in New York City, sections of heavy portable track (along with much other improvised technology) helped in the epic move of the ancient obelisk in Central Park to its final location from the dock where it was unloaded from the cargo ship "SS Dessoug".


title: Railway track

text: Cane railways often had permanent tracks for the main lines, with portable tracks serving the canefields themselves. These tracks were narrow gauge (for example, ) and the portable track came in straights, curves, and turnouts, rather like on a model railway.


title: Railway track

text: The "permanent way" is so called because "temporary way" tracks were often used in the construction of that permanent way.


title: Railway track

text: The geometry of the tracks is three-dimensional by nature, but the standards that express the speed limits and other regulations in the areas of track gauge, alignment, elevation, curvature and track surface are usually expressed in two separate layouts for horizontal and vertical.


title: Railway track

text: Horizontal layout is the track layout on the horizontal plane. This involves the layout of three main track types: "tangent track" (straight line), "curved track", and "track transition curve" (also called "transition spiral" or "spiral") which connects between a tangent and a curved track.


title: Railway track

text: Vertical layout is the track layout on the vertical plane including the concepts such as crosslevel, cant and gradient.


title: Railway track

text: A "sidetrack" is a railroad track other than siding that is auxiliary to the main track. The word is also used as a verb (without object) to refer to the movement of trains and railcars from the main track to a siding, and in common parlance to refer to giving in to distractions apart from a main subject. Sidetracks are used by railroads to order and organise the flow of rail traffic.


title: Railway track

text: During the early days of rail, there was considerable variation in the gauge used by different systems. , about 60% of the world's railways use a gauge of , known as standard or international gauge Gauges wider than standard gauge are called broad gauge; narrower, narrow gauge. Some stretches of track are dual gauge, with three (or sometimes four) parallel rails in place of the usual two, to allow trains of two different gauges to use the same track.


title: Railway track

text: Gauge can safely vary over a range. For example, U.S. federal safety standards allow standard gauge to vary from to for operation up to .


title: Railway track

text: Track needs regular maintenance to remain in good order, especially when high-speed trains are involved. Inadequate maintenance may lead to a "slow order" (North American terminology, or temporary speed restriction in the United Kingdom) being imposed to avoid accidents (see Slow zone). Track maintenance was at one time hard manual labour, requiring teams of labourers, or trackmen (US: gandy dancers; UK: platelayers; Australia: fettlers), who used lining bars to correct irregularities in horizontal alignment (line) of the track, and tamping and jacks to correct vertical irregularities (surface). Currently, maintenance is facilitated by a variety of specialised machines.


title: Railway track

text: Common maintenance jobs include changing sleepers, lubricating and adjusting switches, tightening loose track components, and surfacing and lining track to keep straight sections straight and curves within maintenance limits. The process of sleeper and rail replacement can be automated by using a track renewal train.


title: Railway track

text: Spraying ballast with herbicide to prevent weeds growing through and redistributing the ballast is typically done with a special weed killing train.


title: Railway track

text: Over time, ballast is crushed or moved by the weight of trains passing over it, periodically requiring relevelling ("tamping") and eventually to be cleaned or replaced. If this is not done, the tracks may become uneven, causing swaying, rough riding and possibly derailments. An alternative to tamping is to lift the rails and sleepers and reinsert the ballast beneath. For this, specialist "stoneblower" trains are used.


title: Railway track

text: Rail inspections utilize nondestructive testing methods to detect internal flaws in the rails. This is done by using specially equipped HiRail trucks, inspection cars, or in some cases, handheld inspection devices.


title: Railway track

text: Rails must be replaced before the railhead profile wears to a degree that may trigger a derailment. Worn mainline rails usually have sufficient life remaining to be used on a branch line, siding or stub afterwards and are "cascaded" to those applications.


title: Railway track

text: The environmental conditions along railroad track create a unique railway ecosystem. This is particularly so in the United Kingdom, where steam locomotives are only used on special services and vegetation has not been trimmed back so thoroughly. This creates a fire risk in prolonged dry weather.


title: Railway track

text: In the UK, the cess is used by track repair crews to walk to a work site, and as a safe place to stand when a train is passing. This helps when doing minor work, while needing to keep trains running, by not needing a Hi-railer or transport vehicle blocking the line to transport crew to get to the site.


title: Railway track

text: Railway tracks are generally laid on a bed of stone track ballast or track bed, which in turn is supported by prepared earthworks known as the track formation. The formation comprises the subgrade and a layer of sand or stone dust (often sandwiched in impervious plastic), known as the blanket, which restricts the upward migration of wet clay or silt. There may also be layers of waterproof fabric to prevent water penetrating to the subgrade. The track and ballast form the . The foundation may refer to the ballast and formation, i.e. all man-made structures below the tracks.


title: Railway track

text: Some railroads are using asphalt pavement below the ballast in order to keep dirt and moisture from moving into the ballast and spoiling it. The fresh asphalt also serves to stabilize the ballast so it does not move around so easily.


title: Railway track

text: Additional measures are required where the track is laid over permafrost, such as on the Qingzang Railway in Tibet. For example, transverse pipes through the subgrade allow cold air to penetrate the formation and prevent that subgrade from melting.


title: Railway track

text: Geosynthetics are used to reduce or replace traditional layers in trackbed construction and rehabilitation worldwide to improve track support and reduce track maintenance costs. Reinforcement geosynthetics, such as geocells (which rely on 3D soil confinement mechanisms) have demonstrated efficacy in stabilizing soft subgrade soils and reinforcing substructural layers to limit progressive track degradation. Reinforcement geosynthetics increase soil bearing capacity, limit ballast movement and degradation and reduce differential settlement that affects track geometry. They also reduce construction time and cost, while reducing environmental impact and carbon footprint. The increased use of geosynthetic reinforcement solutions is supported by new high-performance geocell materials (e.g., NPA - Novel Polymeric Alloy), published research, case studies projects and international standards (ISO, ASTM, CROW/SBRCURnet)


title: Railway track

text: The hybrid use of high-performance geogrids at the subgrade and high-performance geocell in the upper subbase/subballast layer has been shown to increase the reinforcement factor greater than their separate sums, and is particularly effective in attenuating heaving of expansive subgrade clay soils. A field test project on Amtrak's NE Corridor suffering clay mud-pumping demonstrated how the hybrid solution improved track quality index (TQI) significantly reduced track geometry degradation and lowered track surface maintenance by factor of 6.7x utilizing high-performance NPA geocell. Geosynthetic reinforcement is also used to stabilize railway embankments, which must be robust enough to withstand repeated cyclical loading. Geocells can utilize recycled marginal or poorly graded granular material to create stable embankments, make railway construction more economical and sustainable.


title: Railway track

text: Some buses can use tracks. This concept came out of Germany and was called . The first such track, the O-Bahn Busway, was built in Adelaide, Australia.


title: The Fame Game (TV series)

text: The Fame Game is an Indian Hindi-language family thriller drama streaming television series on Netflix created by Sri Rao and directed by Bejoy Nambiar and Karishma Kohli. Produced by Karan Johar and Somen Mishra under the banner Dharmatic Entertainment, the series stars Madhuri Dixit, Sanjay Kapoor, Manav Kaul, Suhasini Mulay, Lakshvir Saran and Muskkaan Jaferi in lead roles.


title: The Fame Game (TV series)

text: The series revolves around a Bollywood actress named Anamika Anand who suddenly goes missing one day.


title: The Fame Game (TV series)

text: Anamika Anand is a Bollywood star who has a glamorous career and a seemingly idyllic family - but there is more to her personal life than meets the eye. She is physically and verbally abused by her husband, Nikhil More. While her daughter Amara aspires to be a great star like her mother, highlighting nepotism in the current Bollywood industry, her son Avi has his own issues to face including his sexuality. Additionally, Anamika’s mother consistently berates her and other members of the family and uses manipulative techniques to achieve her goals. Her only solace is Manish Khanna, her frequent co-star and past lover. Anamika's sudden disappearance puts her personal life in the limelight and thus begins the quest to find her and the person behind her disappearance, which leads to the unveiling of many dark secrets.


title: The Fame Game (TV series)

text: The official song video "Dupatta Mera" focuses on the dance performance of Madhuri Dixit, while the promotional video also features Varun Dhawan, Siddharth Malhotra, Ishaan Khatter, Riteish Deshmukh, Jackie Shroff and Johnny Lever.


title: The Fame Game (TV series)

text: Announced in May 2020 with the title "Finding Anamika", the show was eventually renamed as "The Fame Game".


title: The Fame Game (TV series)

text: Madhuri Dixit was cast in the titular role, and was joined by Sanjay Kapoor and Manav Kaul as the leads. The cast also included Lakshvir Saran and Muskkaan Jaferi as Madhuri’s character’s children.


title: The Fame Game (TV series)

text: The series received positive reviews from critics. India TV gave the series 3 and a half stars out of five and wrote 'Madhuri Dixit, Sanjay Kapoor and ensemble deliver pitch-perfect family drama'. It further added 'The Fame Game on Netflix takes the dysfunctional family trope and packs it with suspense and drama, making it an enjoyable and binge-worthy series.


title: The Fame Game (TV series)

text: Koimoi gave the series 3 stars and wrote 'Madhuri Dixit Nene convincingly becomes a mystery dressed in uncertain layers playing an extension to her real self'. The review further praised the writer Sri Rao's script by calling it impeccable, perfect and idealistic. Saibal Chatterjee of NDTV too gave it 3 stars and wrote 'The Incandescence Of Madhuri Dixit - Dive Right In'. He praised Dixit's performance by saying 'She gets into the skin of the protagonist with such dazzling panache that the line separating the character from the performer is frequently breached'. Sukanya Verma of Rediff gave the series 3 and Half stars and wrote 'What The Fame Game showcases is the depth and marvels of Madhuri as she switches between star and human, mother and woman'.


title: Tracey Thorn

text: Tracey Anne Thorn (born 26 September 1962) is a British singer. She is best known as being one half of the duo Everything but the Girl from 1982 to 1999. She was a member of the band Marine Girls between 1980 and 1983 and since 2007 has been active as a solo artist.


title: Tracey Thorn

text: The youngest of three children, Thorn was born in Brookmans Park, Hertfordshire. She grew up in nearby Hatfield and studied English at the University of Hull, where she graduated in 1984 with First Class Honours. She later took an MA degree at Birkbeck, University of London.


title: Tracey Thorn

text: Thorn began her musical career in the punk-pop hybrid group Stern Bops playing guitar and providing some vocal backing.


title: Tracey Thorn

text: Thorn then formed Marine Girls as primary songwriter, playing guitar and sharing vocals. The band released two albums ("Beach Party" in 1981 and "Lazy Ways" in 1983) and three singles. The group disbanded in 1983.


title: Tracey Thorn

text: Thorn met Ben Watt at the University of Hull where they were both students, and both signed as solo artists to Cherry Red Records. Their first album together was "Eden", released in 1984. Everything but the Girl released a body of work that spanned two decades. Their biggest chart success came in 1995, when DJ Todd Terry remixed a song from their "Amplified Heart" album. "Missing" peaked at number three on the UK Singles Chart, topped the charts in countries such as Canada, Denmark, Germany and Italy and peaked within the top ten of the charts in many countries, including Australia, France, the Republic of Ireland, Sweden and the United States.


title: Tracey Thorn

text: Everything but the Girl has been inactive since 2000. Watt has played on some filmed performances of Thorn's solo work and on her 2011 recording of the xx's "Night Time".


title: Tracey Thorn

text: Thorn's first solo work was a mini-album entitled "A Distant Shore" (1982). A re-recorded version of the track "Plain Sailing" was released as a single, and was included on the "Pillows & Prayers" Cherry Red records compilation album.


title: Tracey Thorn

text: In the 1980s, Thorn contributed guest vocals and backing vocals for The Style Council on the track "The Paris Match" (from the album "Café Bleu"), The Go-Betweens on their track "Head Full of Steam", Working Week on the single "Venceremos (We Will Win)" and Lloyd Cole and the Commotions on the track "Big Snake".


title: Tracey Thorn

text: In the 1990s, she collaborated with Massive Attack on several projects, including the soundtrack for the motion picture "Batman Forever" where she contributed with "The Hunter Gets Captured by the Game". Their first project together was the song "Protection" (for which she wrote the lyrics and melody) from the album by Massive Attack of the same name. She also co-wrote and sings on the track "Better Things". She also sang "The Tree Knows Everything" on Adam F's debut album, "Colours".


title: Tracey Thorn

text: Just prior to her return to recording in 2007, Thorn contributed vocals to the song "Damage" by the band Tiefschwarz on the album "Eat Books".


title: Tracey Thorn

text: In March 2007, Tracey Thorn released her second solo album "Out of the Woods" on Virgin Records (Worldwide) and on Astralwerks (USA). It was produced by Ewan Pearson, who kept collaborating with her in subsequent releases. The first single from the album, "It's All True", accompanied by remixes from the likes of Kris Menace & Martin Buttrich, was released on 7 February and reached No. 75 on the UK singles chart while the album met critical acclaim and peaked at No. 38 on the Albums Chart.


title: Tracey Thorn

text: In 2008, Thorn collaborated with the Hungarian acoustic downtempo group The Unbending Trees on their single "Overture", which also featured on their album "Chemically Happy (Is The New Sad)", released by her partner Ben Watt.


title: Tracey Thorn

text: In 2009, Thorn collaborated with the Swedish singer-songwriter Jens Lekman for a cover of The Magnetic Fields' "Yeah! Oh Yeah!" for a compilation album commemorating twenty years of Merge Records, "Score! 20 Years of Merge Records: The Covers!".


title: Tracey Thorn

text: Thorn's third solo album "Love and Its Opposite" was released in May 2010 on Ben Watt's Strange Feeling Records in the UK, and on Merge Records in the US. Recorded in London and Berlin and produced by Ewan Pearson, it contained eight new songs and two cover versions, "Come on Home to Me" by Lee Hazlewood, and "You Are a Lover" by The Unbending Trees.


title: Tracey Thorn

text: Thorn's fourth solo album was a Christmas album entitled "Tinsel and Lights". It was released in late October 2012, and included covers of songs by Carol Hall, The White Stripes, Ron Sexsmith, Randy Newman, Joni Mitchell, Sufjan Stevens, Low and Scritti Politti, plus two original songs and contributions from Green Gartside and Ben Watt. The original song "Joy" is featured in the 2012 film "All Is Bright" with Paul Giamatti and Paul Rudd.


title: Tracey Thorn

text: In 2013 Thorn wrote and recorded the original music for "The Falling", the debut feature film by filmmaker Carol Morley, which premiered at the London Film Festival 2014.


title: Tracey Thorn

text: A compilation album, "", was released in the UK on 23 October 2015. It features 34 tracks on two discs.


title: Tracey Thorn

text: On 17 January 2018, Thorn announced the release of her album "Record", which was released on 2 March. The album was produced by Ewan Pearson, and features contributions from Corinne Bailey Rae, Shura, Jona Ma and Stella and Jenny from Warpaint. Along with the announcement, Thorn released the debut single and video from the project, entitled "Queen".


title: Tracey Thorn

text: Virago published Thorn's memoir "Bedsit Disco Queen: How I Grew Up and Tried to Be a Pop Star" early in 2013. It received widespread critical acclaim and was a "Sunday Times" Top Ten best-seller.


title: Tracey Thorn

text: In 2014, she began a regular column ('Off the Record') for the "New Statesman". The column ran until spring of 2022.


title: Tracey Thorn

text: 2021 saw the publication of a fourth book, "My Rock 'n' Roll Friend", focused on her friendship with Lindy Morrison of the Go-Betweens, and on the experiences of female musicians in the male-dominated music scene.


title: Tracey Thorn

text: After 28 years as a couple, Thorn and the other half of Everything But The Girl, Ben Watt, married in 2009 at Chelsea Register Office. They live in Hampstead, North London. The couple have twin girls, Jean and Alfie, born in 1998.


title: American Truck Simulator

text: American Truck Simulator is a truck simulator game developed and published by SCS Software. It was announced as being in development in September 2013 and unveiled at the E3 2015. It was released on 2 February 2016 for Microsoft Windows, Linux, and macOS. The game is the parallel sequel to "Euro Truck Simulator 2", the spiritual successor of "18 Wheels of Steel", and the third installment in the "Truck Simulator" series. Set in a condensed depiction of United States, the player can drive one of a choice of American-style conventional trucks, visiting various locations across the U.S., picking up a variety of cargos, and delivering them to their destinations.


title: American Truck Simulator

text: "American Truck Simulator" is a truck driving simulator with business management elements. A beginning player will be directed to found a truck driving business and select a home city from which to operate that business. Upon selection of the home city, the player will own the pre-placed truck garage located in that city, which will operate as the player's home base.


title: American Truck Simulator

text: During gameplay, the player will select from a menu of currently available goods delivery routes to drive one of several models of trailer-hooked truck and deliver the selected load to a designated location within a fixed amount of time. By making such deliveries, the player earns money for the player's company and experience points for the player themself. By delivering the selected cargo to its designation within the allotted time and with the least damage to the goods, the player will maximize the amount of money and experience points earned. Late deliveries or deliveries with damage will result in the player earning reduced cash and experience points. The amount of money and experience points earned are commensurate to the length of the delivery in distance traveled and type of goods being transported.


title: American Truck Simulator

text: A beginning player will own a garage, but no trucks or trailers. The player will begin by completing "quick jobs," which are goods deliveries that utilize an in-game company's trucks and trailers. Once the player has earned enough money, the player may then begin purchasing one or more trucks, but the player may continue making "quick job" deliveries if desired. After purchasing a truck, the player may elect to use the purchased truck for deliveries, or go back to performing quick job deliveries.


title: American Truck Simulator

text: As the player completes deliveries, the player will unlock skills by spending experience points to purchase particular skills upgrades. These upgrade categories include fuel efficiency, route delivery distance, carrying heavy cargo, carrying dangerous goods, carrying fragile cargoes, or making urgent deliveries.


title: American Truck Simulator

text: The money earned by the player's company will automatically be used to pay back any company loans the player obtains for the company or to pay any fines incurred in the course of the player's gameplay. The money is also needed to pay for fuel and maintenance on any vehicles or trailers owned by the player's company. When performing quick job deliveries using an in-game company's truck, repairs and other costs are paid by that in-game company and not from the funds of the player's company. The player may also use the company's money to purchase additional trucks and trailers which are held in designated slots in the garage.


title: American Truck Simulator

text: The player may use company funds to hire NPC drivers (and pay their associated expenses), who are placed in additional driver slots in the garage. Once the player has earned sufficient money, the player may also purchase garages in other cities and hire NPC drivers to drive from those garages, as well. The longer an NPC driver is employed by the company, the more experience points they will earn, thus increasing the amount of money that driver earns from each delivery. Much like the player's experience points, the player may direct the focus of each hired driver's experience points, thereby ensuring that particular hired drivers become experts in particular skill areas, such as hauling dangerous goods or performing long-haul deliveries.


title: American Truck Simulator

text: Company money may be used to upgrade garages, which will allow the garages to hold additional trucks, trailers, and NPC drivers, as well as place a reduced-cost fueling station at the garage. The company money may be used to upgrade the company's trucks and trailers, specifically by upgrading their associated aesthetic, mechanical, and structural upgrades.


title: American Truck Simulator

text: While driving routes, the game will direct the player to stop at designated weigh stations to determine the weight of the cargo before being permitted to proceed (though the game may occasionally allow the driver to bypass such station). When crossing the border into the state of California (currently only in the northern part of the state), the player is similarly obliged to stop at California Border Protection Stations to have their vehicle inspected. Avoiding a weigh station or border protection station will result the player being fined.


title: American Truck Simulator

text: SCS Software confirmed in a blog post on 15 February 2016 that the Kenworth W900 has been launched and added to the game. Later, the company confirmed in a blog post that the Peterbilt 579 and the Kenworth T680 will ship with the sim on release day. They also confirmed the Peterbilt 389 on 3 November 2016. Two years later, SCS Software included the Volvo VNL into the game on 5 November 2018. A little over a year later, on 10 December 2019, the CEO of SCS Software confirmed that the International LoneStar would be coming to the game. The LoneStar was released into the game on 12 December 2019. Four months later on 28 April 2020, the Mack Anthem was added to the game, with the Western Star 49X being added to the game 4 months later on 30 September 2020, about one day later after its real-world unveiling. Then three months later on 2 December 2020, the Freightliner Cascadia was added to the game.


title: American Truck Simulator

text: A little less than a year later, on 1 September 2021, SCS added to the International line in game with the International LT, formerly known as the International ProStar, which accompanies the International LoneStar. Three months later, the Freightliner Cascadia received an update with new parts from the 2022 model of the truck. On March 22, 2022, The International 9900i was added to the game. On August 2, 2022, Western Star Trucks unveiled the new Western Star 57X truck, with SCS announcing shortly afterwards that the truck was also available in the game.


title: American Truck Simulator

text: The game is currently set in a condensed 1:20-scaled version of the entire Western Contiguous and part of the South Central regions in the United States, expanded periodically by the developer through downloadable content. It currently features depictions of the western U.S. states of California, Nevada, Arizona, with New Mexico, Oregon, Washington, Utah, Idaho, Colorado, Wyoming, Montana and Texas available as DLCs. The game features 181 visitable cities, including most state capitals and major cities, as well as many thousands of miles worth of in-game roads. Currently, the player may travel as far north as Bellingham, Washington, as far south as Brownsville, Texas, as far west as Eureka, California, and as far east as Beaumont, Texas, assuming the player has all the states available to them. SCS have stated that most future map expansions, if not all, will be at additional cost.


title: American Truck Simulator

text: The modding community for American Truck Simulator have also created their own map extensions. The most popular of these extensions include cities in each state, Mexico, and Canada, though the majority of these maps, with some exceptions, are generally not as dense with roads as the base game nor regarded by the community as high quality or detailed. Some modded maps redo older sections of the map with their own areas, regarded as higher quality than the vanilla game. These old areas are generally considered to be out-of-date by the community, with lower design standards than SCS Software's map content with the exception of northern California and Las Vegas as of version 1.44.


title: American Truck Simulator

text: The game started off at launch with the U.S. states of California and Nevada, and expanded from there, with Arizona being added in June 2016 as a free update. A number of other states like Utah have now been added as paid DLC:


title: American Truck Simulator

text: On 11 April 2014, SCS Software announced that there will be 100+ cities in the game once completed (not initially), and SCS released screenshots of the game. Truck brands included on "American Truck Simulator" so far are Kenworth, Peterbilt, Volvo, International Trucks, Western Star, Mack and Freightliner. More will follow; the only setback remains the licensing of trucks from their manufacturers. SCS plans to eventually include the entire contiguous United States, as long as the game continues to do well. On 26 January 2015, SCS Software published a one-hour video to YouTube of footage from early alpha of the game. On 18 December 2015, SCS Software announced the official release date for "American Truck Simulator", 3 February 2016, on their blog. The game was released one day earlier instead.


title: American Truck Simulator

text: "American Truck Simulator" has received mostly positive reviews from critics, scoring 76/100 on Metacritic.


title: American Truck Simulator

text: James Cunningham of "Hardcore Gamer" gave the game a 4 out of 5 saying, "While a little more realism would make "American Truck Simulator" more fun, paradoxical as that may sound, there’s no escaping how fantastically playable it is." Laura Dale from Polygon rated the game a 8/10 saying, "As someone who sunk countless hours into "Euro Truck Simulator 2", a fresh coat of paint, an unfamiliar set of sights and the challenge of driving on the wrong opposite side of the road left me confident that I'll be sinking just as many hours into "American Truck Simulator"."


title: American Truck Simulator

text: Andy Kelly of "PC Gamer" commended the game and noted that it shared the strengths and shortcomings of its predecessor due to the two games' similarities, though advised that it was not finished on launch and urged more cautious gamers to wait until it was more completed before purchasing the game.


title: American Truck Simulator

text: "American Truck Simulator" won Best technological solution at the 2016 Czech Game of the Year Awards, and was also nominated for Best Game, Best PC/Console Game, and Best Audio.


title: Loop quantum gravity

text: Loop quantum gravity (LQG) is a theory of quantum gravity, which aims to merge quantum mechanics and general relativity, incorporating matter of the Standard Model into the framework established for the pure quantum gravity case. It is an attempt to develop a quantum theory of gravity based directly on Einstein's geometric formulation rather than the treatment of gravity as a force. As a theory LQG postulates that the structure of space and time is composed of finite loops woven into an extremely fine fabric or network. These networks of loops are called spin networks. The evolution of a spin network, or spin foam, has a scale above the order of a Planck length, approximately 10 meters, and smaller scales are meaningless. Consequently, not just matter, but space itself, prefers an atomic structure.


title: Loop quantum gravity

text: The areas of research, which involves about 30 research groups worldwide, share the basic physical assumptions and the mathematical description of quantum space. Research has evolved in two directions: the more traditional canonical loop quantum gravity, and the newer covariant loop quantum gravity, called spin foam theory. The most well-developed theory that has been advanced as a direct result of loop quantum gravity is called loop quantum cosmology (LQC). LQC advances the study of the early universe, incorporating the concept of the Big Bang into the broader theory of the Big Bounce, which envisions the Big Bang as the beginning of a period of expansion that follows a period of contraction, which one could talk of as the "Big Crunch."


title: Loop quantum gravity

text: In 1986, Abhay Ashtekar reformulated Einstein's general relativity in a language closer to that of the rest of fundamental physics, specifically Yang–Mills theory. Shortly after, Ted Jacobson and Lee Smolin realized that the formal equation of quantum gravity, called the Wheeler–DeWitt equation, admitted solutions labelled by loops when rewritten in the new Ashtekar variables. Carlo Rovelli and Smolin defined a nonperturbative and background-independent quantum theory of gravity in terms of these loop solutions. Jorge Pullin and Jerzy Lewandowski understood that the intersections of the loops are essential for the consistency of the theory, and the theory should be formulated in terms of intersecting loops, or graphs.


title: Loop quantum gravity

text: In 1994, Rovelli and Smolin showed that the quantum operators of the theory associated to area and volume have a discrete spectrum. That is, geometry is quantized. This result defines an explicit basis of states of quantum geometry, which turned out to be labelled by Roger Penrose's spin networks, which are graphs labelled by spins.


title: Loop quantum gravity

text: The canonical version of the dynamics was established by Thomas Thiemann, who defined an anomaly-free Hamiltonian operator and showed the existence of a mathematically consistent background-independent theory. The covariant, or "spin foam", version of the dynamics was developed jointly over several decades by research groups in France, Canada, UK, Poland, and Germany. It was completed in 2008, leading to the definition of a family of transition amplitudes, which in the classical limit can be shown to be related to a family of truncations of general relativity. The finiteness of these amplitudes was proven in 2011. It requires the existence of a positive cosmological constant, which is consistent with observed acceleration in the expansion of the Universe.


title: Loop quantum gravity

text: LQG is formally background independent. Meaning the equations of LQG are not embedded in, or dependent on, space and time (except for its invariant topology). Instead, they are expected to give rise to space and time at distances which are 10 times the Planck length. The issue of background independence in LQG still has some unresolved subtleties. For example, some derivations require a fixed choice of the topology, while any consistent quantum theory of gravity should include topology change as a dynamical process.


title: Loop quantum gravity

text: Space-time as a "container" over which physics takes place has no objective physical meaning and instead the gravitational interaction is represented as just one of the fields forming the world. This is known as the relationalist interpretation of space-time. In LQG this aspect of general relativity is taken seriously and this symmetry is preserved by requiring that the physical states remain invariant under the generators of diffeomorphisms. The interpretation of this condition is well understood for purely spatial diffeomorphisms. However, the understanding of diffeomorphisms involving time (the Hamiltonian constraint) is more subtle because it is related to dynamics and the so-called "slave nature of time" in general relativity. A generally accepted calculational framework to account for this constraint has yet to be found. A plausible candidate for the quantum Hamiltonian constraint is the operator introduced by Thiemann.


title: Loop quantum gravity

text: The constraints define a constraint surface in the original phase space. The gauge motions of the constraints apply to all phase space but have the feature that they leave the constraint surface where it is, and thus the orbit of a point in the hypersurface under gauge transformations will be an orbit entirely within it. Dirac observables are defined as phase space functions, formula_1, that Poisson commute with all the constraints when the constraint equations are imposed,


title: Loop quantum gravity

text: that is, they are quantities defined on the constraint surface that are invariant under the gauge transformations of the theory.


title: Loop quantum gravity

text: Then, solving only the constraint formula_3 and determining the Dirac observables with respect to it leads us back to the Arnowitt–Deser–Misner (ADM) phase space with constraints formula_4. The dynamics of general relativity is generated by the constraints, it can be shown that six Einstein equations describing time evolution (really a gauge transformation) can be obtained by calculating the Poisson brackets of the three-metric and its conjugate momentum with a linear combination of the spatial diffeomorphism and Hamiltonian constraint. The vanishing of the constraints, giving the physical phase space, are the four other Einstein equations.


title: Loop quantum gravity

text: Many of the technical problems in canonical quantum gravity revolve around the constraints. Canonical general relativity was originally formulated in terms of metric variables, but there seemed to be insurmountable mathematical difficulties in promoting the constraints to quantum operators because of their highly non-linear dependence on the canonical variables. The equations were much simplified with the introduction of Ashtekar's new variables. Ashtekar variables describe canonical general relativity in terms of a new pair of canonical variables closer to those of gauge theories. The first step consists of using densitized triads formula_5 (a triad formula_6 is simply three orthogonal vector fields labeled by formula_7 and the densitized triad is defined by formula_8) to encode information about the spatial metric,


title: Loop quantum gravity

text: (where formula_10 is the flat space metric, and the above equation expresses that formula_11, when written in terms of the basis formula_6, is locally flat). (Formulating general relativity with triads instead of metrics was not new.) The densitized triads are not unique, and in fact one can perform a local in space rotation with respect to the internal indices formula_13. The canonically conjugate variable is related to the extrinsic curvature by formula_14. But problems similar to using the metric formulation arise when one tries to quantize the theory. Ashtekar's new insight was to introduce a new configuration variable,


title: Loop quantum gravity

text: that behaves as a complex formula_16 connection where formula_17 is related to the so-called spin connection via formula_18. Here formula_19 is called the chiral spin connection. It defines a covariant derivative formula_20. It turns out that formula_21 is the conjugate momentum of formula_19, and together these form Ashtekar's new variables.


title: Loop quantum gravity

text: The expressions for the constraints in Ashtekar variables; Gauss's theorem, the spatial diffeomorphism constraint and the (densitized) Hamiltonian constraint then read:


title: Loop quantum gravity

text: respectively, where formula_26 is the field strength tensor of the connection formula_19 and where formula_28 is referred to as the vector constraint. The above-mentioned local in space rotational invariance is the original of the formula_16 gauge invariance here expressed by Gauss's theorem. Note that these constraints are polynomial in the fundamental variables, unlike the constraints in the metric formulation. This dramatic simplification seemed to open up the way to quantizing the constraints. (See the article Self-dual Palatini action for a derivation of Ashtekar's formalism).


title: Loop quantum gravity

text: With Ashtekar's new variables, given the configuration variable formula_30, it is natural to consider wavefunctions formula_31. This is the connection representation. It is analogous to ordinary quantum mechanics with configuration variable formula_32 and wavefunctions formula_33. The configuration variable gets promoted to a quantum operator via:


title: Loop quantum gravity

text: (analogous to formula_37). In passing over to the quantum theory the constraints become operators on a kinematic Hilbert space (the unconstrained formula_16 Yang–Mills Hilbert space). Note that different ordering of the formula_39's and formula_40's when replacing the formula_40's with derivatives give rise to different operators – the choice made is called the factor ordering and should be chosen via physical reasoning. Formally they read


title: Loop quantum gravity

text: There are still problems in properly defining all these equations and solving them. For example, the Hamiltonian constraint Ashtekar worked with was the densitized version instead of the original Hamiltonian, that is, he worked with formula_45. There were serious difficulties in promoting this quantity to a quantum operator. Moreover, although Ashtekar variables had the virtue of simplifying the Hamiltonian, they are complex. When one quantizes the theory, it is difficult to ensure that one recovers real general relativity as opposed to complex general relativity.


title: Loop quantum gravity

text: The classical result of the Poisson bracket of the smeared Gauss' law formula_46 with the connections is


title: Loop quantum gravity

text: If one smears the quantum Gauss' law and study its action on the quantum state one finds that the action of the constraint on the quantum state is equivalent to shifting the argument of formula_49 by an infinitesimal (in the sense of the parameter formula_50 small) gauge transformation,


title: Loop quantum gravity

text: and the last identity comes from the fact that the constraint annihilates the state. So the constraint, as a quantum operator, is imposing the same symmetry that its vanishing imposed classically: it is telling us that the functions formula_52 have to be gauge invariant functions of the connection. The same idea is true for the other constraints.


title: Loop quantum gravity

text: Therefore, the two step process in the classical theory of solving the constraints formula_53 (equivalent to solving the admissibility conditions for the initial data) and looking for the gauge orbits (solving the 'evolution' equations) is replaced by a one step process in the quantum theory, namely looking for solutions formula_49 of the quantum equations formula_55. This is because it obviously solves the constraint at the quantum level and it simultaneously looks for states that are gauge invariant because formula_56 is the quantum generator of gauge transformations (gauge invariant functions are constant along the gauge orbits and thus characterize them). Recall that, at the classical level, solving the admissibility conditions and evolution equations was equivalent to solving all of Einstein's field equations, this underlines the central role of the quantum constraint equations in canonical quantum gravity.


title: Loop quantum gravity

text: It was in particular the inability to have good control over the space of solutions to Gauss's law and spatial diffeomorphism constraints that led Rovelli and Smolin to consider the loop representation in gauge theories and quantum gravity.


title: Loop quantum gravity

text: LQG includes the concept of a holonomy. A holonomy is a measure of how much the initial and final values of a spinor or vector differ after parallel transport around a closed loop; it is denoted


title: Loop quantum gravity

text: Knowledge of the holonomies is equivalent to knowledge of the connection, up to gauge equivalence. Holonomies can also be associated with an edge; under a Gauss Law these transform as


title: Loop quantum gravity

text: and is called a Wilson loop. Thus Wilson loops are gauge invariant. The explicit form of the Holonomy is


title: Loop quantum gravity

text: where formula_65 is the curve along which the holonomy is evaluated, and formula_66 is a parameter along the curve, formula_67 denotes path ordering meaning factors for smaller values of formula_66 appear to the left, and formula_69 are matrices that satisfy the formula_16 algebra


title: Loop quantum gravity

text: The Pauli matrices satisfy the above relation. It turns out that there are infinitely many more examples of sets of matrices that satisfy these relations, where each set comprises formula_72 matrices with formula_73, and where none of these can be thought to 'decompose' into two or more examples of lower dimension. They are called different irreducible representations of the formula_16 algebra. The most fundamental representation being the Pauli matrices. The holonomy is labelled by a half integer formula_75 according to the irreducible representation used.


title: Loop quantum gravity

text: The use of Wilson loops explicitly solves the Gauss gauge constraint. Loop representation is required to handle the spatial diffeomorphism constraint. With Wilson loops as a basis, any Gauss gauge invariant function expands as,


title: Loop quantum gravity

text: This is called the loop transform and is analogous to the momentum representation in quantum mechanics (see Position and momentum space). The QM representation has a basis of states formula_77 labelled by a number formula_78 and expands as


title: Loop quantum gravity

text: one should define the corresponding operator formula_84 on formula_85 in the loop representation via,


title: Loop quantum gravity

text: A transformation formula giving the action of the operator formula_84 on formula_85 in terms of the action of the operator formula_82 on formula_52 is then obtained by equating the R.H.S. of formula_93 with the R.H.S. of formula_94 with formula_95 substituted into formula_94, namely


title: Loop quantum gravity

text: where formula_99 means the operator formula_82 but with the reverse factor ordering (remember from simple quantum mechanics where the product of operators is reversed under conjugation). The action of this operator on the Wilson loop is evaluated as a calculation in the connection representation and the result is rearranged purely as a manipulation in terms of loops (with regard to the action on the Wilson loop, the chosen transformed operator is the one with the opposite factor ordering compared to the one used for its action on wavefunctions formula_52). This gives the physical meaning of the operator formula_84. For example, if formula_103 corresponded to a spatial diffeomorphism, then this can be thought of as keeping the connection field formula_39 of formula_63 where it is while performing a spatial diffeomorphism on formula_65 instead. Therefore, the meaning of formula_84 is a spatial diffeomorphism on formula_65, the argument of formula_85.


title: Loop quantum gravity

text: In the loop representation, the spatial diffeomorphism constraint is solved by considering functions of loops formula_85 that are invariant under spatial diffeomorphisms of the loop formula_65. That is, knot invariants are used. This opens up an unexpected connection between knot theory and quantum gravity.


title: Loop quantum gravity

text: Any collection of non-intersecting Wilson loops satisfy Ashtekar's quantum Hamiltonian constraint. Using a particular ordering of terms and replacing formula_21 by a derivative, the action of the quantum Hamiltonian constraint on a Wilson loop is


title: Loop quantum gravity

text: When a derivative is taken it brings down the tangent vector, formula_114, of the loop, formula_65. So,


title: Loop quantum gravity

text: However, as formula_26 is anti-symmetric in the indices formula_118 and formula_119 this vanishes (this assumes that formula_65 is not discontinuous anywhere and so the tangent vector is unique).


title: Loop quantum gravity

text: With regard to loop representation, the wavefunctions formula_85 vanish when the loop has discontinuities and are knot invariants. Such functions solve the Gauss law, the spatial diffeomorphism constraint and (formally) the Hamiltonian constraint. This yields an infinite set of exact (if only formal) solutions to all the equations of quantum general relativity! This generated a lot of interest in the approach and eventually led to LQG.


title: Loop quantum gravity

text: The easiest geometric quantity is the area. Let us choose coordinates so that the surface formula_122 is characterized by formula_123. The area of small parallelogram of the surface formula_122 is the product of length of each side times formula_125 where formula_126 is the angle between the sides. Say one edge is given by the vector formula_127 and the other by formula_128 then,


title: Loop quantum gravity

text: In the space spanned by formula_130 and formula_131 there is an infinitesimal parallelogram described by formula_132 and formula_133. Using formula_134 (where the indices formula_39 and formula_136 run from 1 to 2), yields the area of the surface formula_122 given by


title: Loop quantum gravity

text: where formula_139 and is the determinant of the metric induced on formula_122. The latter can be rewritten formula_141 where the indices formula_142 go from 1 to 2. This can be further rewritten as


title: Loop quantum gravity

text: There is a similarity between this and the expression for formula_145. But in Ashtekar variables, formula_146. Therefore,


title: Loop quantum gravity

text: According to the rules of canonical quantization the triads formula_148 should be promoted to quantum operators,


title: Loop quantum gravity

text: The area formula_150 can be promoted to a well defined quantum operator despite the fact that it contains a product of two functional derivatives and a square-root. Putting formula_151 (formula_152-th representation),


title: Loop quantum gravity

text: The quantization of the volume proceeds the same way as with the area. Each time the derivative is taken, it brings down the tangent vector formula_114, and when the volume operator acts on non-intersecting Wilson loops the result vanishes. Quantum states with non-zero volume must therefore involve intersections. Given that the anti-symmetric summation is taken over in the formula for the volume, it needs intersections with at least three non-coplanar lines. At least four-valent vertices are needed for the volume operator to be non-vanishing.


title: Loop quantum gravity

text: Assuming the real representation where the gauge group is formula_16, Wilson loops are an over complete basis as there are identities relating different Wilson loops. These occur because Wilson loops are based on matrices (the holonomy) and these matrices satisfy identities. Given any two formula_16 matrices formula_162 and formula_163,


title: Loop quantum gravity

text: where by formula_168 we mean the loop formula_166 traversed in the opposite direction and formula_170 means the loop obtained by going around the loop formula_65 and then along formula_166. See figure below. Given that the matrices are unitary one has that formula_173. Also given the cyclic property of the matrix traces (i.e. formula_174) one has that formula_175. These identities can be combined with each other into further identities of increasing complexity adding more loops. These identities are the so-called Mandelstam identities. Spin networks certain are linear combinations of intersecting Wilson loops designed to address the over-completeness introduced by the Mandelstam identities (for trivalent intersections they eliminate the over-completeness entirely) and actually constitute a basis for all gauge invariant functions.


title: Loop quantum gravity

text: As mentioned above the holonomy tells one how to propagate test spin half particles. A spin network state assigns an amplitude to a set of spin half particles tracing out a path in space, merging and splitting. These are described by spin networks formula_65: the edges are labelled by spins together with 'intertwiners' at the vertices which are prescription for how to sum over different ways the spins are rerouted. The sum over rerouting are chosen as such to make the form of the intertwiner invariant under Gauss gauge transformations.


title: Loop quantum gravity

text: In the long history of canonical quantum gravity formulating the Hamiltonian constraint as a quantum operator (Wheeler–DeWitt equation) in a mathematically rigorous manner has been a formidable problem. It was in the loop representation that a mathematically well defined Hamiltonian constraint was finally formulated in 1996. We leave more details of its construction to the article Hamiltonian constraint of LQG. This together with the quantum versions of the Gauss law and spatial diffeomorphism constrains written in the loop representation are the central equations of LQG (modern canonical quantum General relativity).


title: Loop quantum gravity

text: Finding the states that are annihilated by these constraints (the physical states), and finding the corresponding physical inner product, and observables is the main goal of the technical side of LQG.


title: Loop quantum gravity

text: A very important aspect of the Hamiltonian operator is that it only acts at vertices (a consequence of this is that Thiemann's Hamiltonian operator, like Ashtekar's operator, annihilates non-intersecting loops except now it is not just formal and has rigorous mathematical meaning). More precisely, its action is non-zero on at least vertices of valence three and greater and results in a linear combination of new spin networks where the original graph has been modified by the addition of lines at each vertex together and a change in the labels of the adjacent links of the vertex.


title: Loop quantum gravity

text: In loop quantum gravity (LQG), a spin network represents a "quantum state" of the gravitational field on a 3-dimensional hypersurface. The set of all possible spin networks (or, more accurately, "s-knots" – that is, equivalence classes of spin networks under diffeomorphisms) is countable; it constitutes a basis of LQG Hilbert space.


title: Loop quantum gravity

text: In physics, a spin foam is a topological structure made out of two-dimensional faces that represents one of the configurations that must be summed to obtain a Feynman's path integral (functional integration) description of quantum gravity. It is closely related to loop quantum gravity.


title: Loop quantum gravity

text: On this section see and references therein. The Hamiltonian constraint generates 'time' evolution. Solving the Hamiltonian constraint should tell us how quantum states evolve in 'time' from an initial spin network state to a final spin network state. One approach to solving the Hamiltonian constraint starts with what is called the Dirac delta function. The summation of which over different sequences of actions can be visualized as a summation over different histories of 'interaction vertices' in the 'time' evolution sending the initial spin network to the final spin network. Each time a Hamiltonian operator acts it does so by adding a new edge at the vertex.


title: Loop quantum gravity

text: This then naturally gives rise to the two-complex (a combinatorial set of faces that join along edges, which in turn join on vertices) underlying the spin foam description; we evolve forward an initial spin network sweeping out a surface, the action of the Hamiltonian constraint operator is to produce a new planar surface starting at the vertex. We are able to use the action of the Hamiltonian constraint on the vertex of a spin network state to associate an amplitude to each "interaction" (in analogy to Feynman diagrams). See figure below. This opens up a way of trying to directly link canonical LQG to a path integral description. Now just as a spin networks describe quantum space, each configuration contributing to these path integrals, or sums over history, describe 'quantum space-time'. Because of their resemblance to soap foams and the way they are labeled John Baez gave these 'quantum space-times' the name 'spin foams'.


title: Loop quantum gravity

text: There are however severe difficulties with this particular approach, for example the Hamiltonian operator is not self-adjoint, in fact it is not even a normal operator (i.e. the operator does not commute with its adjoint) and so the spectral theorem cannot be used to define the exponential in general. The most serious problem is that the formula_177's are not mutually commuting, it can then be shown the formal quantity formula_178 cannot even define a (generalized) projector. The master constraint (see below) does not suffer from these problems and as such offers a way of connecting the canonical theory to the path integral formulation.


title: Loop quantum gravity

text: It turns out there are alternative routes to formulating the path integral, however their connection to the Hamiltonian formalism is less clear. One way is to start with the BF theory. This is a simpler theory than general relativity, it has no local degrees of freedom and as such depends only on topological aspects of the fields. BF theory is what is known as a topological field theory. Surprisingly, it turns out that general relativity can be obtained from BF theory by imposing a constraint, BF theory involves a field formula_179 and if one chooses the field formula_136 to be the (anti-symmetric) product of two tetrads


title: Loop quantum gravity

text: (tetrads are like triads but in four spacetime dimensions), one recovers general relativity. The condition that the formula_136 field be given by the product of two tetrads is called the simplicity constraint. The spin foam dynamics of the topological field theory is well understood. Given the spin foam 'interaction' amplitudes for this simple theory, one then tries to implement the simplicity conditions to obtain a path integral for general relativity. The non-trivial task of constructing a spin foam model is then reduced to the question of how this simplicity constraint should be imposed in the quantum theory. The first attempt at this was the famous Barrett–Crane model. However this model was shown to be problematic, for example there did not seem to be enough degrees of freedom to ensure the correct classical limit. It has been argued that the simplicity constraint was imposed too strongly at the quantum level and should only be imposed in the sense of expectation values just as with the Lorenz gauge condition formula_183 in the Gupta–Bleuler formalism of quantum electrodynamics. New models have now been put forward, sometimes motivated by imposing the simplicity conditions in a weaker sense.


title: Loop quantum gravity

text: Another difficulty here is that spin foams are defined on a discretization of spacetime. While this presents no problems for a topological field theory as it has no local degrees of freedom, it presents problems for GR. This is known as the problem triangularization dependence.


title: Loop quantum gravity

text: Just as imposing the classical simplicity constraint recovers general relativity from BF theory, one expects an appropriate quantum simplicity constraint will recover quantum gravity from quantum BF theory.


title: Loop quantum gravity

text: Much progress has been made with regard to this issue by Engle, Pereira, and Rovelli, Freidel and Krasnov and Livine and Speziale in defining spin foam interaction amplitudes with much better behaviour.


title: Loop quantum gravity

text: An attempt to make contact between EPRL-FK spin foam and the canonical formulation of LQG has been made.


title: Loop quantum gravity

text: The Classical limit is the ability of a physical theory to approximate classical mechanics. It is used with physical theories that predict non-classical behavior. Any candidate theory of quantum gravity must be able to reproduce Einstein's theory of general relativity as a classical limit of a quantum theory. This is not guaranteed because of a feature of quantum field theories which is that they have different sectors, these are analogous to the different phases that come about in the thermodynamical limit of statistical systems. Just as different phases are physically different, so are different sectors of a quantum field theory. It may turn out that LQG belongs to an unphysical sector – one in which one does not recover general relativity in the semiclassical limit (in fact there might not be any physical sector at all).


title: Loop quantum gravity

text: Moreover, the physical Hilbert space formula_184 must contain enough semiclassical states to guarantee that the quantum theory one obtains can return to the classical theory when formula_185. In order to guarantee this one must avoid quantum anomalies at all cost, because if we do not there will be restrictions on the physical Hilbert space that have no counterpart in the classical theory, implying that the quantum theory has fewer degrees of freedom than the classical theory.


title: Loop quantum gravity

text: Theorems establishing the uniqueness of the loop representation as defined by Ashtekar et al. (i.e. a certain concrete realization of a Hilbert space and associated operators reproducing the correct loop algebra – the realization that everybody was using) have been given by two groups (Lewandowski, Okolow, Sahlmann and Thiemann; and Christian Fleischhack). Before this result was established it was not known whether there could be other examples of Hilbert spaces with operators invoking the same loop algebra – other realizations not equivalent to the one that had been used so far. These uniqueness theorems imply no others exist, so if LQG does not have the correct semiclassical limit then the theorems would mean the end of the loop representation of quantum gravity altogether.


title: Loop quantum gravity

text: There are a number of difficulties in trying to establish LQG gives Einstein's theory of general relativity in the semiclassical limit:


title: Loop quantum gravity

text: Difficulties in trying to examine the semiclassical limit of the theory should not be confused with it having the wrong semiclassical limit.


title: Loop quantum gravity

text: Concerning issue number 2 above, one can consider so-called weave states. Ordinary measurements of geometric quantities are macroscopic, and planckian discreteness is smoothed out. The fabric of a T-shirt is analogous: at a distance it is a smooth curved two-dimensional surface, but on closer inspection we see that it is actually composed of thousands of one-dimensional linked threads. The image of space given in LQG is similar. Consider a very large spin network formed by a very large number of nodes and links, each of Planck scale. Probed at a macroscopic scale, it appears as a three-dimensional continuous metric geometry.


title: Loop quantum gravity

text: To make contact with familiar low energy physics it is mandatory to have to develop approximation schemes both for the physical inner product and for Dirac observables; the spin foam models that have been intensively studied can be viewed as avenues toward approximation schemes for said physical inner product.


title: Loop quantum gravity

text: Markopoulou, et al. adopted the idea of noiseless subsystems in an attempt to solve the problem of the low energy limit in background independent quantum gravity theories The idea has even led to the intriguing possibility of matter of the standard model being identified with emergent degrees of freedom from some versions of LQG (see section below: "LQG and related research programs").


title: Loop quantum gravity

text: completely determine the theory. In particular, one can calculate the scattering amplitudes from these quantities. As explained below in the section on the "Background independent scattering amplitudes", in the background-independent context, the formula_188 point functions refer to a state and in gravity that state can naturally encode information about a specific geometry which can then appear in the expressions of these quantities. To leading order, LQG calculations have been shown to agree in an appropriate sense with the formula_188point functions calculated in the effective low energy quantum general relativity.


title: Loop quantum gravity

text: Thiemann's Master Constraint Programme for Loop Quantum Gravity (LQG) was proposed as a classically equivalent way to impose the infinite number of Hamiltonian constraint equations in terms of a single master constraint, which involves the square of the constraints in question. An initial objection to the use of the master constraint was that on first sight it did not seem to encode information about the observables; because the Master constraint is quadratic in the constraint, when one computes its Poisson bracket with any quantity, the result is proportional to the constraint, therefore it always vanishes when the constraints are imposed and as such does not select out particular phase space functions. However, it was realized that the condition is equivalent to being a Dirac observable. So the master constraint does capture information about the observables. Because of its significance this is known as the master equation.


title: Loop quantum gravity

text: That the master constraint Poisson algebra is an honest Lie algebra opens up the possibility of using a certain method, known as group averaging, in order to construct solutions of the infinite number of Hamiltonian constraints, a physical inner product thereon and Dirac observables via what is known as refined algebraic quantization, or RAQ.


title: Loop quantum gravity

text: What is done first is, we are able to compute the matrix elements of the would-be operator formula_199, that is, we compute the quadratic form formula_200. It turns out that as formula_200 is a graph changing, diffeomorphism invariant quadratic form it cannot exist on the kinematic Hilbert space formula_202, and must be defined on formula_203. Since the master constraint operator formula_199 is densely defined on formula_205, then formula_199 is a positive and symmetric operator in formula_205. Therefore, the quadratic form formula_200 associated with formula_199 is closable. The closure of formula_200 is the quadratic form of a unique self-adjoint operator formula_211, called the Friedrichs extension of formula_199. We relabel formula_211 as formula_199 for simplicity.


title: Loop quantum gravity

text: Note that the presence of an inner product, viz Eq 4, means there are no superfluous solutions i.e. there are no formula_49 such that


title: Loop quantum gravity

text: It is also possible to construct a quadratic form formula_218 for what is called the extended master constraint (discussed below) on formula_202 which also involves the weighted integral of the square of the spatial diffeomorphism constraint (this is possible because formula_218 is not graph changing).


title: Loop quantum gravity

text: The spectrum of the master constraint may not contain zero due to normal or factor ordering effects which are finite but similar in nature to the infinite vacuum energies of background-dependent quantum field theories. In this case it turns out to be physically correct to replace formula_199 with formula_222 provided that the "normal ordering constant" vanishes in the classical limit, that is,


title: Loop quantum gravity

text: The constraints in their primitive form are rather singular, this was the reason for integrating them over test functions to obtain smeared constraints. However, it would appear that the equation for the master constraint, given above, is even more singular involving the product of two primitive constraints (although integrated over space). Squaring the constraint is dangerous as it could lead to worsened ultraviolet behaviour of the corresponding operator and hence the master constraint programme must be approached with due care.


title: Loop quantum gravity

text: In doing so the master constraint programme has been satisfactorily tested in a number of model systems with non-trivial constraint algebras, free and interacting field theories. The master constraint for LQG was established as a genuine positive self-adjoint operator and the physical Hilbert space of LQG was shown to be non-empty, an obvious consistency test LQG must pass to be a viable theory of quantum General relativity.


title: Loop quantum gravity

text: The master constraint has been employed in attempts to approximate the physical inner product and define more rigorous path integrals.


title: Loop quantum gravity

text: The Consistent Discretizations approach to LQG, is an application of the master constraint program to construct the physical Hilbert space of the canonical theory.


title: Loop quantum gravity

text: It turns out that the master constraint is easily generalized to incorporate the other constraints. It is then referred to as the extended master constraint, denoted formula_226. We can define the extended master constraint which imposes both the Hamiltonian constraint and spatial diffeomorphism constraint as a single operator,


title: Loop quantum gravity

text: Setting this single constraint to zero is equivalent to formula_228 and formula_229 for all formula_194 in formula_122. This constraint implements the spatial diffeomorphism and Hamiltonian constraint at the same time on the Kinematic Hilbert space. The physical inner product is then defined as


title: Loop quantum gravity

text: (as formula_233). A spin foam representation of this expression is obtained by splitting the formula_234-parameter in discrete steps and writing


title: Loop quantum gravity

text: The spin foam description then follows from the application of formula_236 on a spin network resulting in a linear combination of new spin networks whose graph and labels have been modified. Obviously an approximation is made by truncating the value of formula_237 to some finite integer. An advantage of the extended master constraint is that we are working at the kinematic level and so far it is only here we have access semiclassical coherent states. Moreover, one can find none graph changing versions of this master constraint operator, which are the only type of operators appropriate for these coherent states.


title: Loop quantum gravity

text: The master constraint programme has evolved into a fully combinatorial treatment of gravity known as algebraic quantum gravity (AQG). The non-graph changing master constraint operator is adapted in the framework of algebraic quantum gravity. While AQG is inspired by LQG, it differs drastically from it because in AQG there is fundamentally no topology or differential structure – it is background independent in a more generalized sense and could possibly have something to say about topology change. In this new formulation of quantum gravity AQG semiclassical states always control the fluctuations of all present degrees of freedom. This makes the AQG semiclassical analysis superior over that of LQG, and progress has been made in establishing it has the correct semiclassical limit and providing contact with familiar low energy physics.


title: Loop quantum gravity

text: Black hole thermodynamics is the area of study that seeks to reconcile the laws of thermodynamics with the existence of black hole event horizons. The no hair conjecture of general relativity states that a black hole is characterized only by its mass, its charge, and its angular momentum; hence, it has no entropy. It appears, then, that one can violate the second law of thermodynamics by dropping an object with nonzero entropy into a black hole. Work by Stephen Hawking and Jacob Bekenstein showed that one can preserve the second law of thermodynamics by assigning to each black hole a "black-hole entropy"


title: Loop quantum gravity

text: where formula_39 is the area of the hole's event horizon, formula_240 is the Boltzmann constant, and formula_241 is the Planck length. The fact that the black hole entropy is also the maximal entropy that can be obtained by the Bekenstein bound (wherein the Bekenstein bound becomes an equality) was the main observation that led to the holographic principle.


title: Loop quantum gravity

text: An oversight in the application of the no-hair theorem is the assumption that the relevant degrees of freedom accounting for the entropy of the black hole must be classical in nature; what if they were purely quantum mechanical instead and had non-zero entropy? Actually, this is what is realized in the LQG derivation of black hole entropy, and can be seen as a consequence of its background-independence – the classical black hole spacetime comes about from the semiclassical limit of the quantum state of the gravitational field, but there are many quantum states that have the same semiclassical limit. Specifically, in LQG


title: Loop quantum gravity

text: it is possible to associate a quantum geometrical interpretation to the microstates: These are the quantum geometries of the horizon which are consistent with the area, formula_39, of the black hole and the topology of the horizon (i.e. spherical). LQG offers a geometric explanation of the finiteness of the entropy and of the proportionality of the area of the horizon. These calculations have been generalized to rotating black holes.


title: Loop quantum gravity

text: It is possible to derive, from the covariant formulation of full quantum theory (Spinfoam) the correct relation between energy and area (1st law), the Unruh temperature and the distribution that yields Hawking entropy. The calculation makes use of the notion of dynamical horizon and is done for non-extremal black holes.


title: Loop quantum gravity

text: A recent success of the theory in this direction is the computation of the entropy of all non singular black holes directly from theory and independent of Immirzi parameter. The result is the expected formula formula_243, where formula_244 is the entropy and formula_39 the area of the black hole, derived by Bekenstein and Hawking on heuristic grounds. This is the only known derivation of this formula from a fundamental theory, for the case of generic non singular black holes. Older attempts at this calculation had difficulties. The problem was that although Loop quantum gravity predicted that the entropy of a black hole is proportional to the area of the event horizon, the result depended on a crucial free parameter in the theory, the above-mentioned Immirzi parameter. However, there is no known computation of the Immirzi parameter, so it had to be fixed by demanding agreement with Bekenstein and Hawking's calculation of the black hole entropy.


title: Loop quantum gravity

text: A detailed study of the quantum geometry of a black hole horizon has been made using loop quantum gravity. Loop-quantization does not reproduce the result for black hole entropy originally discovered by Bekenstein and Hawking, unless one chooses the value of the Immirzi parameter to cancel out another constant that arises in the derivation. However, it led to the computation of higher-order corrections to the entropy and radiation of black holes.


title: Loop quantum gravity

text: Based on the fluctuations of the horizon area, a quantum black hole exhibits deviations from the Hawking spectrum that would be observable were X-rays from Hawking radiation of evaporating primordial black holes to be observed. The quantum effects are centered at a set of discrete and unblended frequencies highly pronounced on top of Hawking radiation spectrum.


title: Loop quantum gravity

text: In 2014 Carlo Rovelli and Francesca Vidotto proposed that there is a Planck star inside every black hole. Based on LQG, the theory states that as stars are collapsing into black holes, the energy density reaches the Planck energy density, causing a repulsive force that creates a star. Furthermore, the existence of such a star would resolve the black hole firewall and black hole information paradox.


title: Loop quantum gravity

text: The popular and technical literature makes extensive references to LQG-related topic of loop quantum cosmology. LQC was mainly developed by Martin Bojowald, it was popularized in "Scientific American" for predicting a Big Bounce prior to the Big Bang. Loop quantum cosmology (LQC) is a symmetry-reduced model of classical general relativity quantized using methods that mimic those of loop quantum gravity (LQG) that predicts a "quantum bridge" between contracting and expanding cosmological branches.


title: Loop quantum gravity

text: Achievements of LQC have been the resolution of the big bang singularity, the prediction of a Big Bounce, and a natural mechanism for inflation.


title: Loop quantum gravity

text: LQC models share features of LQG and so is a useful toy model. However, the results obtained are subject to the usual restriction that a truncated classical theory, then quantized, might not display the true behaviour of the full theory due to artificial suppression of degrees of freedom that might have large quantum fluctuations in the full theory. It has been argued that singularity avoidance in LQC are by mechanisms only available in these restrictive models and that singularity avoidance in the full theory can still be obtained but by a more subtle feature of LQG.