seems to be working hello students welcome to tonight's class I am your teacher Robin Shaw from Korea I am not Korean I am Canadian but I am living in Korea I hope everyone can hear me and see me well let's take a look at the students that are here I see a lot of students started chatting Kavino hello good to see you again Leila Lollie Lollie is back again okay and Kavino has a question we'll get to your question in a moment after the greeting sleepwalkers here just Tina and Farida hello and that's it all the good students are here the bad students are not here so perfect just gonna open my drink you could notice I shaved today last week I had the beard but today I shaved and my hair is a little messy I need it I need a haircut you know I grow up my hair and my beard and I shave my beard and my hair still a little long I'll get a haircut probably tomorrow or something let's get into Kavino's question and Kavino is asking a dictionary word and as most of you know I do not like let's move that I do not like dictionary words because I'm not a dictionary so Kavino you asked could you answer for this question what is meant by sufficient all right now you shouldn't waste a question asking about a word what you need to do is go to the dictionary so I'm gonna go to the ox oxford learners dictionary and I type in sufficient that's what you need to do and there it is and then right there I just copy that's what it means you can get the pronunciation but I'm gonna copy what it means I'm gonna come over here and paste it so it says let's get rid of it says enough for a particular purpose as much as you need so let's make let's make a dialogue with sufficient mom I need some money mom says here is ten dollars is that sufficient and what does she mean by sufficient let's put that a blue and the key word here is enough so is that sufficient is the same is that enough so the quick answer sufficient is a big word big vocabulary but it just means enough okay so I hope that helps you understand in the future if you have a dictionary word I hope you go to the dictionary first find out what the word means try to make a sentence and then ask me hey Robin check my sentence let's see any other questions questions everyone's saying hello to each other and convenient I'll never ask that kind of dictionary word sir I really don't apologize just learn you have to learn to try and before you just ask the teacher don't waste the teacher's time just try to figure out something else out yourself and then ask the teacher to check ask the teacher to check that's a good way all right let's see what Layla Layla and Lily is that's my phone when when lolly lolly is here I call I call Layla Layla Layla I had an accident so my car is well this is a noun I write off this is a noun I checked in the dictionary you don't check on the dictionary I checked in the dictionary the meaning of write off I found the third meaning isn't related to financial case what do you think well which dictionary did you use write off well could be a phrasal verb there could be a lot of meanings for write off because it's a verb and the preposition off write off that can mean many things but as a noun you're using it as a noun one two three write off noun okay you use this example a period of time I'm not familiar with this one number three an act of canceling a debt that's financial that's financial number two is not financial but I don't use that number three is financial but how you used it here as a noun this is this is the most common way to use write off and write off meaning you cannot repair this car you had an accident a car accident you cannot repair so it's a write off as a noun I write off sleepwalker has a cultural question let's take a look Robin how is February 14th usually celebrated in Korea I heard Japan okay yeah so similar to Japan so actually there's in East Asia I don't know how many countries but certainly Korea probably Japan too February 14th is Valentine's Day and March 14th is something called White Day so Valentine's Day the rule of course you can break the rule women give men chocolate so men do not in in Korea men do not have to do anything on white or Valentine's Day so in in Canada or USA Valentine's Day is when men and women exchange flowers gifts chocolate so it's a day for men and women in like USA Canada probably the UK but in Korea it's a day for men so the the women give men chocolate and then on March 14th that's White Day the rule is men give women candy do they follow this rule well you know of course women might give men candy or food or something else and then on March 14th men excuse me might give women flowers chocolate so yeah this is the this is the the rule but of course it can change a little bit depending but certainly they're very strict that February 14th women give the gift to men March 14th men give women a gift and then April 14th is I believe you know I'm teaching about the culture here is black day and black day is for single people they eat they eat alone dish called jajangmyeon Chinese dish they eat alone on that day or with other single people I don't know exactly but yeah so that's upcoming Valentine's Day women give the men or give me give me maybe a gift and then on March 14th maybe I give a woman a gift and then black day for single people all right I hope that clears it up sleep walker all right so Covino good for you you got an example here let's take a look I have sufficient food to be eaten for my lunch you have food so you don't need to say be eaten I have sufficient food for my lunch but I lost them in that forest all right so because you lost it you have to say I had I no longer have so your example sentence is correct you use sufficient correctly but a sufficient is a big word a little too formal you used it correctly but you know it's better just to say enough if you're talking to your friend you wouldn't say sufficient you would say enough but you you use sufficient correctly there use use a gun hello Frida let's see what Frida is talking about I personally use most used and nuanced expressions that are used by native speakers but honestly don't like to use expression that are rarely used by native speakers that's a good rule use common expressions don't use rare or not common expressions that's a good rule to follow Palavi hello my car is right off my car is written off yes right off VJ so if you use it as a noun my car is off right off and here my car is written off senior Solomon hi everyone okay so sleepwalkers is we don't have a white day in Russia we usually celebrate celebrate International Women's Day on March 8th mark that's you said international I'm gonna check that International Women's Day is March 8th there we go didn't I didn't know that checking that now International Women's Day this year it's March 4th does it change the says March 8th here well that that that advertisement was wrong International Women's Day isn't every day Women's Day we'll just say every every day is Robin's day okay no no I'm not going to say that because then people start messaging me every day sleepwalker wow I hear about a black day for the first time well sleepwalker are you going to celebrate black day this year lally lally Robin please all right please what the project progressed by the day hmm day by day the project progressed same thing no no no no because day by day is very special each day day by day by the day I I'd never heard this expression before so by the day is definitely wrong I've never heard that by the day day by day so number two it's not the answer is no it's not the same meaning number two is the correct meaning and number one I never heard that before so what we day by day the project the pro the project progressed every day the part daily maybe I would just say daily and then it would be right but Molly naturally from Cambodia hello I've been to Cambodia a couple one time or two times I don't remember I traveled a lot at least one time teacher can you teach English me I'm in Cambodia I speak English and listen little well but Molly now Charlie Molly not Charlie let's take a look at I can help you fix up your sentence spelling English and English to me let's put a period I'm Cambodian and Khmer period I can speak English and listen a little so you want to say a little period I'm what's wrong here I'm Campbell oh I'm from Cambodia or I'm Cambodian teacher can you teach English to me and they're suggesting you know teach me English which would probably be better yeah uh yeah that's what I do here but Molly not Charlie if you have any questions about English just let me know and I'll do my best to teach you I don't always have the answer but I will try my best sir what is IELTS test well it's funny you're asking about IELTS and I'll talk about IELTS today I opened a new YouTube channel if you're in the WhatsApp group you saw my link to my new YouTube YouTube channel it just opened so there's nothing there yet I'll talk about it more in the future where I teach IELTS why do you need IELTS well if you plan to work or study in an English speaking country then you need to study IELTS so if you plan to go to America or UK or Canada Australia uh New Zealand to work or to study you need to take a language test and there's two main language tests the IELTS test which is actually developed by the UK and the other one is TOEFL which is USA so these are English language tests uh oh I spelled TOEFL well they're they're not easy they take months and months of study for some people they take years so yeah as I said I started the IELTS channel and I'll start putting up videos there if you do not plan to work or study in another country you do not need to study IELTS act day sounds a little sad depends there's some people that are happy and the is it correct no your answer is not correct I'm trying to think of you can't say he's written off uh you're using a verb now certainly if you use it as a noun use a write off makes sense as a noun as a verb I think it's better to use it in noun form as a verb my computer you could say is a verb uh let's use a past tense my uh my computer I wrote I wrote my computer off with this no a native speaker wouldn't say it this way we're gonna use it in noun form using write off in the verb again I gotta think of the example mm that takes long try to use in a past tense might be easier to use it in past tense so we wrote off the broken computer if you're talking about one or here we wrote off the the computer after it fell to the ground yeah okay we wrote off so here I'm using a verb form we wrote off the computer after it fell to the ground uh noun form makes more sense this one could be a little confusing but this is how you do it I would suggest you stay to the noun form but yeah the you can use the verb form uh Layla have you heard Robin have you uh yes okay so you got sad news Layla Robin have you heard about the Moroccan child who fell into a well yes I did and that's uh the that was big news international news I heard about that it's very sad I don't want to comment on that because it was sad but yeah it's sad sad story Robin send a link of your new channel here uh it's a channel I'm developing with a good friend of mine called James it's not really ready yet because uh because it's not so here let me see if I got any link like we just opened basically today I'll just put a link to the video and then you can there's a link to the IELTS channel Justina says so glad to hear that you opened it is past hence and on IELTS channel so we need that ED and on because channel is a noun I'm looking forward so much about your IELTS channel okay thank you Justina and did I catch up you guys are out of questions all right uh so Layla you responded about the Moroccan child story and I guess I will talk about it I'll just grab a headline from Reuters news all right so the headline here of the newspaper Moroccan boy trapped in well dies before rescue so it's very uh so the boy is trapped in the well they're trying to rescue him for days I believe but they failed he died unfortunately very very sad and Layla you responded yeah exactly okay I am touched after knowing the end of his story now problem here Layla is is touched when you're using touched I'm touched these are more positive uh emotional reactions so if someone does something good for you you're touched you might cry we cry is negative but if you're very very happy or you're touched because someone did something so good for you and you cry that's that's considered a positive thing so uh Layla you made a critical error I don't mean to say critical error but I gotta be careful because uh you cannot say touched when something is tragic so this this is very a tragic story very bad very sad so in in something that's very bad very sad we don't use touched so I am uh okay what could you say maybe a better word might be heartbroken so heartbroken would mean very sad uh it's a very I'm very let's get maybe I'm very uh heartbroken I think heartbroken is a good way to express that touched use for the positive emotional reactions not this case it doesn't work well in this case Layla sleepwalker I usually eat several times during a day or both versions of during and within no you're talking about one day now if we say the day which means in generally now it works for a kind of routine you're I usually is is is talking about a routine so you're not talking about one day you're talking about many days so we just want to be general the day the daytime so I usually eat several times during the day now it works I usually eat several times within a day now it works so are both versions okay during within now the answer is yes I usually I usually eat several times during the day I usually eat several times within a day yep both can work well sleepwalker I'm not hunting for subscribers unless you're interested in aisles Layla is it okay to use fall with illness yes she has fallen ill uh fallen is used with many many expressions as you put there you can fall in love or with many emotions you can fall you can fall ill you can fall into depression these are the three main ones so yeah you can fall in love you can fall ill and you can fall into this depression yep so the answer is yes and your example she has fallen ill she had she has fallen ill she she has fallen ill two days ago okay or we must we can use it with love we can use a love illness and depression thank you Gui and Kavinu hope you will consider about the above request which request I see you deleted your last Kavinu I you deleted you removed your last message so I cannot see what you're asking Kavinu you got to ask again so basically the same things yes I would like to know more about aisles this okay we'll check out the channel teacher can you give example in from positive and negatives well but Molly Nachali what do you mean positive and negative positive and negative what negative what so I am happy that's a positive I am not happy that's a negative so I'm adding not to show negative is that what you mean I'm not sure what you mean by positive and negative I am happy I am not happy she is sad she is not sad there's the negative right there okay so Layla is responding oh no I thought I could use touched with a sad situation as well so I'm sorry for him yeah that that was a big mistake I don't usually tell students that's a big mistake but if you're talking to someone who didn't know you were a student and they said you know something like my father died and yours yes or you just said I'm touched uh yeah this would be very very wrong very wrong this is don't don't use it like I'm touched this way so I thought I would have to it's critical mistake I got to make sure you don't make that mistake with I'm touched do native speakers use dirty as a verb very often for example don't sit on the ground you might dirty your pants sure we use everything as a verb if so this person said spoon me what do they mean spoon me what does that mean mean well we know spoon is for eating that's not a verb that's a noun but if someone said spoon me what do they mean well pass me a spoon so yeah almost everything could be changed into a verb for casual only spoken English of course in an essay or an interview or something formal you would never use verbs and nouns in the wrong way but yes Laila the answer is always going to be yes native speakers use words that are not verbs and they use them as verbs can I use moved instead of heart broke no moved is also moved and touched mean the same thing so moved you're having that emotional reaction that is in a positive way they mean the same thing so you cannot use moved oh we got a big word uh too big for me I don't use it capricious capricious I don't use very often like I said that maybe 25 years ago is it so negative connotation I would say yes I would say yes so someone's capricious for those of you doing showing sudden changes in attitude and behavior or you got a British spelling of behavior let's change it to american so should we use a capricious and let's get the capricious capricious capricious capricious I was saying it wrong because I don't use it capricious so showing sudden changes in attitude and behavior so only with negative connotation so do we only use it in the negative way if we say capricious that means their change was bad I would say yes I don't know if that's a rule I like your sentence this is how I would use it it's hard to do business with this person he is capricious that is correct it's hard to do business with him because he has sudden changes in attitude and behavior so I'm gonna say yes use it more with an always with a negative I don't want to use the word always but I think it's always in a negative connotation uh yeah lately you can say I'm shocked shocked is shocked yes gotta go to my school without getting at least even my breakfast day before yesterday sir what do you think about the sense of momentum could I get it from the past too this is a little confusing gata is not a word in english got two is the word I got to go to my school without getting at least even my breakfast day before yesterday so right here it's confusing I'm not understanding and you're using it without eating my breakfast I gotta without eating at least I have I got to go to school without even eating my breakfast all right day before yet the day before yesterday I had to go to school I had to go to my school we could just say I had to go to school without even eating my breakfast the day before yesterday okay I fixed this up I don't know if this is the correct way of how you want to explain I had to go to school I had to go to school without even eating my breakfast the day before yesterday okay so what's your question what would you think about the sentence which I mentioned okay could I get it for the past too this has to be past tense presence because you said the day the day before yesterday is past tense you're talking about the past this can only be expressed in the past tense present tense if it's a usual routine routine I have to go to school without even eating my breakfast don't put time now it's present tense because we have no time reference it's like a routine so you would say like usually I have to go to school so you gotta use this sentence or this sentence this is past tense this is present tense I had to go to school without even eating my the day before yesterday okay hope that helps Covino I'm not sure if your sentence a little long so it's hard to know what you're talking about spoon me means carry me no spoon me doesn't mean carry me instead of heartbroken I can say affected there's a thousand words you can say are you gonna ask me about every words now you now you're not confident about your English just don't use touched or moved so that news shocked me affected me upset me it goes on you can use almost everything you know so you're now you're focusing on what can I use you can use all these words don't worry about it just you can't use you can't use two words touched me moved me michelle I'm I'm there I'm late welcome michelle the sad story struck me yeah you could say that in a more poetic way that sad stories struck me hit me you you're going into more spoken English that sad story I might say here's another expression hit me hard and this hit me hard or struck or hit me hard means yeah it affected me emotionally deep deeply that sad story hit me deeply you could use that something like that for Rita your meal or eat your meal which one is correct they are both correct we use two verbs so you can say I have lunch or I eat lunch you can use so have your meal you have or eat that works with food both are okay I feel if you want to emphasize about our sadness heartbroken yeah I think heartbroken emphasizes your sad uh like touched you want to emphasize the emotional impact in a positive way but yeah heartbroken the emotional impact in a negative way let's go back to the Moroccan boy they keep saying Moroccan boy does uh does he have a name yes he has a name so we should honor him by learning his name right and his name is Roy Ann Oram and he was five years old so poor uh Ray Ann Oram I hope I'm pronouncing it correctly so he fell into the well and they tried to get him out uh sad story so the best word I would say to use in this situation is tragic because he fell into the well and he was alive he didn't die immediately and you know everyone tried to save him everyone had hope and they tried to save him but they they failed he died so uh very tragic this is very tragic this sort of situation people tried so hard and they put in their effort but still failed very tragic ended in death very sad uh to Ryan Ryan or or or man Oram sorry Ryan Oram tragic when I feel pain in my whole body could I say I am painting no well you're using like a uh now you're very good Layla because you're trying to be like a native speaker and trying to make your own English but that's difficult because I think you need to be fluent or native speaker to have that ability to know exactly how when and where to make your own language which so in this case it's no native speakers would not express themselves like this um now can we use pain as a verb he pains me is maybe possible not using it as a ing here you have two verbs here I am in painting not using it in this case but he pains me can be more uh possible he's causing you pain he pains me all right and sleepwalker responds about the boy Ryan Oram it's a shame good expression I haven't heard that story yeah that story is it's not on the main it's not on the main like if I go to CNN or BBC let's see check BBC now like I don't see I don't see it as top story it's kind of a small story but I guess it because it's from Morocco and not many people know or are interested in Morocco these days but uh yeah it's it's it's international news now uh sleeper I'm hurting yeah this is a verb but she's she's trying to change pain let's layl asking he started for the door we got to go just had another column the old year thimble I feel he started for the door means he started from the door he started for the door all right he started for the door means he started to walk towards the door so when a native speaker says he started for the door or he started for the the building just means he started to walk that way towards the door the building whatever that's all that means uh Farida well this is what we're talking about uh Farida as far as I know pain is just a noun it cannot be used as a verb right if that is the rule but native speakers you know in every language you're you're changing the language and sometimes native speakers use nouns as verbs but uh generally speaking yeah you are correct but a native speaker might break this rule that what about if I say that illness caused caused pain well it's a noun it's used as a noun here in whole you know in my whole body so this is possible that illness caused pain this is not uh this is a noun this is not a verb in my whole body causes okay that illness causes pain in my whole body so you can cause pain you can cause that now Robin what are you drinking energy drink no that well now it's time for our advertisement we are not supported by uh Pepsi zero sugar so like a diet Pepsi lime flavor they do not sponsor this video if I had Pepsi if I had Pepsi sponsorship I'd be drinking in it and you guys should buy it but they don't sponsor me so don't buy that don't buy Pepsi Pepsi Pepsi what do you what do you usually drink sleepwalker I'm not I drinks I want to I drink tea and coffee and I want to drink more tea less coffee and uh yeah I like to drink these cola drinks which is a bad habit that's going to kill me okay sleepwalker says I like drinking tea before sleep or eat an apple sleepwalker you are healthy you're a healthy person healthier than me oh leila has the best question in my live stream ever you got two questions do you think okay I'll fix that do you think if we talk to native speakers and we we're gonna put make uh uh make a big oh okay use and we I'm still gonna change it we make big mistakes do they laugh at us this is very important question very very important when you make big mistakes are native speakers going to laugh at you well yes and no so I'm gonna say no they're not gonna laugh at you if those native speakers are used used to other accents or people from other countries like me I'm used to it I talk to people from all around the world every day and I hear all kinds of mistakes I never laugh it's not funny uh maybe once a year some student says something and it is funny and I might laugh but most of the time I'm not laughing I know I understand the mistakes and well educated people they're well educated they're usually respectful but not everyone is this there are people that will laugh uh young people so kids teenagers even young adults uh racist people there's people that are don't like you because you're different uh they will laugh they will they might make fun of you so uh I I think there's more good people than bad people so I think I'd like to think most people will not laugh at you but you might uh you might excuse me that Pepsi don't drink Pepsi you might meet bad people and use you make a mistake and they make fun of it uh so in Korea yeah sometimes you know when I speak Korean and I make a mistake uh yes some people have made fun of my mistake made fun of my accent pronunciation the words I use uh some Koreans have made fun of me teased me and it's not a good feeling it's not a good feeling so I don't want to tell you everyone is nice not everyone is nice I want to tell you I think most people are nice uh but not everyone's nice so do you think if we talk to native speakers we make big mistakes do they laugh at us depends who you talk to but I think Leila everyone you talk to is going to be nice so I wouldn't I don't think it's a big problem for you Farida are you interested in any k-pop groups uh yay I I liked k-pop when I was younger from maybe 1999 to 2006 so Farida yeah a long time ago I liked k-pop k-pop was very different during this time modern k-pop k-pop these days I'm too old I'm too old for that so I don't uh I don't do you like k-pop Farida I'm not a BTS fan and what's this VJ hey man can we say my body is aching that's a question and you're the answer yes yes you can my body oh my body is aching my body is aching so you have a lot of pain yes Robin I drink also enough often Pepsi without sugar oh michelle it's bad bad for us we have to stop drink tea Sandeep Kumar kindly describe I saw a saw which could not saw okay let's take a look Sandeep I saw a saw which could not saw what's the meaning of this sentence okay so we have to we have to understand that C past past tense is saw so it's meaning one of saw meaning to can we import image okay we can insert an image I've never done this but I'm going to insert it just give me a moment it's the first time I'm importing image there we have an image I move it I saw as a as a noun there we go saw as a verb okay so we need to know these three uses of saw so let's start off I saw past tense I see I saw here we have a noun this tool I saw a saw which could not saw now saw as a verb so my you know I'm going to big screen I don't I don't have a saw so imagine this is a saw the saw is used for cutting wood so as a noun it is a saw but also the action when you're doing this action with a saw the action is called saw as a verb so I am sawing the wood so going back to the sentence I saw a saw which could not saw it's difficult to explain I thought it'd be easier to explain but it's difficult so you got to know the three different ways so see past tense saw I saw yesterday what did I see this this tool a saw and I don't know why they put not you could just play saw the action as a verb saw cutting all right Sandeep I hope that helps don't laugh at people with laugh with them don't laugh with depends who they are Robin are you well Robin do you do we're going to put change that to do you and I'm going to switch these words do you understand well when you understand do you under do you understand well when you speak Korean in a story example no from 1999 when I first came to Korea to about 2016 I studied Korean and I used it I used it a lot I used not you know every day I had to speak some Korean I was not top level Korean but every day I had to use it but society changed in 2016 what changed one big change is phones so we can do more things by phone instead of talking to people so for example I can order things online I don't have to go to the shop I can pay I don't have to go to the bank I can just pay my bills so because of the phone there's a lot of reasons I don't need to talk to any people anymore and also in my area a lot of stores don't have clerks so some stores one store across from my house I go into the store there's no clerk just I pick up my item and I scan it myself and I pay with my card so I don't have to speak to anyone and also restaurants these days they usually have a machine and you order your food and then they cook your food and then your number comes up you just go out and get it so since since about 2016 I don't need to speak Korean anymore because I'm dealing with machines there's very rare human to human contact contact so if I order food or I go to the coffee shop usually I'm ordering on the machine and the machines have English function so I go to the machine English order I never talk to anyone so I don't speak Korean anymore I don't need to and I just forgetting every day forgetting every day Sunday anyone have English WhatsApp group please we have English WhatsApp let's take a look at our WhatsApp groups well time's almost over I just loaded up this is one WhatsApp group for and I just made an IELTS group too nobody's in the IELTS group except Leila there is the first one is English the second one is IELTS Mohammed Diagana are you here are you watching let's see if anyone joins those groups in the next 10 seconds Farida came into the IELTS group I'm watching there's there's no activity in the IELTS group yet all right Mohammed thanks my buddy my supporter let's see what you got to say here well good morning Robin Shaw and everyone I'm back YouTube classes it's been a long time welcome back ask any questions my friend all right I gotta go back here I didn't answer every question sleepwalker how many people speak English in daily life ingredient maybe do you use it Koreans don't speak English Koreans don't speak English the answer is a bad old saw that doesn't cut yeah that that's correct pj thanks my case I try to be more comfortable I know some people who don't want to talk to other be they're afraid to make big mistakes well never be afraid to be make mistakes when you're practicing English you have to make mistakes you will not get better by not making good I don't have time for shy people I only have time for people willing to make mistakes Farida oh talking about kpop yes I'm really interested in kpop I'm not a fan of any particular band like BTS or Blackpink but I always listen to their songs sounds like you're a fan these days thousands of teens are interested in kpop like me thousands millions kpop is big yeah I'm not a fan I don't even I don't listen to BTS or Blackpink not I'm too old but I understand you Farida I understand many people like kpop by the way Reese will who says Kaviru by the way recently a sheet filled by that kind of sentences will receive for you through WhatsApp when you are having a free time can that be checked out sir please what do you mean sheet paper homework I don't really teach in WhatsApp so convenient you can try it doesn't mean I'll do that I re-answer that you're back thank you Farida I'm planning on learning Korean Japanese of the future maybe in a few months why focus on English and reading reading reading so I guess if I live in Korea it would be hard making friends it is hard to make Korean friends it is hard it is very hard and Layla because you're covered up so visibly you look different it would be hard to make friends Koreans are not very open-minded in for global friends oh glee you look younger without a beard and your eyes your eyes are beautiful thank you I wish I could see you oh my screen is not moving let's see if I can fix my screen sometimes my screen locks yeah I'm not sure why screen is not moving let me see if I can I fixed it before well I guess we'll end the live stream here because the screen is not moving so I'm sorry guys it was it was nice talking to you while I could but my camera is broken let me try one more thing yeah I know it's not moving I can see it not moving I don't know why still not moving you can see me it is just not moving all right we'll have to end there that's a bad way to end anyway thank you very much I guess I will see if I can fix that camera issue before next week so if you're listening right now thanks for watching it's time to end anyways it's over an hour I'm starting to get tired so I'll see you next week yep Mohammed I turned it off and on many times it's just not working for some reason all right I'll see you guys next week


What's up everybody? Jayz here for jasperjasecasebrakes.com. Last break of the night. This is the show of the 1920 Panini Impeccable Basketball. It's a three box case break Random teams number eight, and this is an early bird break. So if you buy one of the first 20 spots sold You get a chance to win a free spot Since we actually did a couple of pack fillers There was only actually 15 total spots sold straight up So we're just gonna do the 15 customer names and then number one after the randomizer gets the early bird free So we use the same dice roller for the early bird the customer names And then if you have your name in there with cello forty four forty five You're in there because of a cello pack everybody else bottom straight up and then there are the teams here. Let's paste them And our last case of impeccable. Let's see we can end it off with a huge bang at the end of the night So let's roll it We got ourselves a two and a three for five times number one gets a free spot one two three four and five Wow last spot mojo five times Boom Chris you got a free spot man Boom, that's awesome. All right five times now here on the teams one two three four and five Sean down to David five times one two three four and five Nick's down at 76ers So Sean you have the nicks Danny with the magic gay with the bulls Danny with the T-wolves Richard you have the Kings Kevin with the nuggets Aaron you have the heat Joe with the Suns Ryan you have the blazers Chris last one module thunder Sean with the wizards Chris Clippers Hugh with the cows Aaron you have the Memphis Grizzlies David with the Pacers Ryan You have the raptors Brandon with the nets Daniel with the Hornets Jun Yen with the bucks Chris your free spots Dallas Mavericks Sean with the jazz Hugh with the pistons Ryan with the Celtics Gabe you have the spurs Renee bought straight up got the pelicans That's both the Warriors Danny have the Lakers to with the Rockets all area of the Hawks and David with the 76ers So if anybody wants to trade guys, I'll give you guys a minute or so for trades if not we're breaking Yeah, the water went down the wrong pipe All right We're just gonna go to trade with a man All right, I should okay see wouldn't be too bad in this D-con maybe not now But Darius Basley has been playing pretty well for the okc Thunder. I think you had like 24 points today Which I didn't even know but I seem today yet 24 points and then looked in the stats and like oh He's actually playing pretty decent. Are you in Seattle Danny? I think you are right Yeah, I was just thinking I was like oh, I'm sorry man.  Honestly Not that I was stuck down with Seattle But I just like the color green like I don't know if you heard that before but so I like the Seattle Sonics But when they left okay, see I just continued to like the Thunder Which I know if I probably was from Seattle and I love the Sonics. I probably be hating the Thunder too, but You probably hate me for saying that either way, but I Still refer the Thunder at least But see what actually happened though. Does Seattle really not want to get a new team new rent you new renovations or what? Like what happened there, you know weren't the kings gonna go to Seattle one point You know like What really happened that really left let them go to okay, see But like see that's what I'm saying It's Sacramento stepped up and decided to get a new arena or help out right the city But back back in 0506 or 0607 This Seattle just really not have the money to like get a new stadium or did they just not want to have a team there anymore? I'm Marcus all I don't remember. I was pretty young when that happened, but Just always wonder Calvin Johnson tonight, you know San Antonio Spurs is going to gave but I think Seattle have a team soon though It just fits so perfectly to expand the 32 teams. You just probably have to move okay, see to the west I mean sorry to the east because if Vegas or Seattle were to have a team How are you gonna have all those teams over there? And I feel like you should expand Vegas should have the Vegas should have a basketball team too. They're they're such a big city now Yeah, I'm putting New Orleans probably in the east and there you go you move New Orleans and Okay, see to the east just cuz they're kind of ready borderline, you know in the middle And then you put Seattle in there and then you put The new team with Vegas in there, too Gotcha also the owner didn't like that the city would wouldn't put any money. So he sold them And then the new owner decided to just move him, right? Well, you can't really hate the thunder them or do you hate the new owner for taking them away from Seattle? Mark Price for the Cavs the 99 Cavaliers going to Hugh remember redemption I heard to you guys, but I'll leave that to you Jalen Rose for the Bulls 41 out of 49 Gabe oh with a tease Michele Alexander Walker, it's a red Plate stainless steel or stainless stars, and that's 37 out of 60 Gotcha, gotcha. No, I feel you D cons me. I don't blame me. I don't blame you for doing that But at the same time if the city didn't want to put any money into it. I mean how how's that gonna happen, right? It's kind of like Oakland right the Oakland situation. It's like Oakland didn't want to put any money Into their stadium into their city there so Oakland was pretty forced to move and it's same thing with the Chargers You know they were just very forced to move because the city of San Diego and I didn't want to want to help out And it always comes down to money, you know, Nikolai Lucic 26 out of 49 Orlando magic that's going to Danny rookie autographs car number 130 J a and Jackson Hayes There you go two pelicans in this box All we need to get is uh, it's on and we hit the trifecta Unless we get Nikolameli or something You mean ducks like Oregon ducks decoders. You mean ducks like ducks Definitely don't like that on ducks Oregon I guess because Probably like the Huskies or you like the Huskies or do you like wazoo? Oh John Moran? How about that? That is 99 out of 99 for you eBay 101 mojoes. There you go Memphis Grizz is gonna air and pee I might pay for the spot right there For the spot of admission or price of admission and we got a one-of-one. How about that little base Andrew Wiggins? Ah, sorry about that deacons Well, don't worry deacons. I'm not that kind of fan. Those are the fans. We don't want it any sport You know, I actually just let the field do the talking. You know what I mean? That's right. Deacons wanted to trade the T-wills, right?  That's going to Daniel and the Lucic. That's right. That's right Kyrie Irving For Brooklyn going to Brandon Redemption. Thank God it was a reduction. We got Ernie the Gregorio 12 out of 25 Buffalo Braves See who that goes to. I forget which one were the Clippers Clippers or Buffalo Braves of the Clippers are okay. All right. Thank you The Kentucky Colonel's are the one that have no affiliation with ATEEN. That's right Dave Cohen's Illustrious Inc. 8 out of 10 Nice autograph too. Celtics. It's going to Ryan Schachter. So yeah, Braves out to go to Chris We got Keldon Johnson 24 out of 25 for the Spurs Going to Gate. I'm the last one here before the Redemption He's the out of 99. Deandre Hunter. Stainless Stars. Lana Hawks going to Oliver Yeah, Keldon Johnson actually out of the three rookies is playing really well, right? rookie autographs hollow silver card number 129 J. Oh Jordan Jordan pool very nice Golden State Warriors that's going to pass well Last box and then we still have the metal card depending on where he goes Ray I think this should be pretty big. I honestly think he is gonna be really really good I said it before a couple years ago I felt like he was gonna be the best ball brother Because he got to play with the older ball brothers as a freshman in high school And it's pretty much playing against really good talent really really young So I think as long as he goes to the right team, he should be able to ball and then he's grown to like a six foot seven like you know point guard and Just got him better. And I think what a smart decision, you know going to to Australia right where the plane overseas play professional for a year Playing with grown man that definitely helped him a lot. So I hope he does well out of I hope he does 76 is going to David Yeah, if you listen to the Knicks, I Don't know. What do you go to the Knicks? Isn't RJ a point guard, too? I mean, I think you can't have two point guards or two two of them play on the same floor I mean he could Victor Oladipo, I mean you have West brick and Harden pretty much playing the same floor, right? at a 75 Oladipo Pacers What a David. Yeah, I Mean, yeah, they're pretty marketable. That's for sure. So you get a player like him Definitely helps Kobe white 47 out of 99 Bulls it's going to Gabe another Ben Simmons One out of 49 All right cars kind of coming up a little bit there, but that's Tyrone Lou 10 out of 99 Show that on the video when a Dan T Yeah, he's just not yeah, he's just not the fool like franchise player, you know He'll always be like a good player on the court, but you need like You know you need someone someone different. You got Brad Daughtery Tonight and I Honestly, dude, I would go to RJ 2d cons I feel like we didn't really get to see so much of him the Knicks are not that good So, I don't know man. I really feel like RJ Barrett is gonna get slept on big time And as you can see some second-year players, I've just shot up So I would just I would definitely start like a little small PC R. J. Barrett. I Feel like his stuff might just skyrocket and and it could you know Alan Houston speaking of some Knicks to 80 or I'm sorry two out of 25 All you have to do is just start balling a little bit and then that's it We got a Dylan Wendler Nice little patch auto three color patch 14 out of 25 for the Cleveland Cavaliers Hugh with that one and the last one don't look D cons Darius Basley 42 out of 99 like I said, I think had like 20 plus points today for the Thunder Chris last Balmoja and the last say it officially the metal card Good luck. Yeah, this case wasn't the best case of course, but Sometimes just just goes that way actually don't speak too soon Kevin This will make it up. Oh My god, it's definitely made the case right here. This is a four out of eight LeBron James and it's a gold for the Lakers Dan T with the Lakers. Well, yeah, this is like three four thousand dollars right there That'll definitely make up the case right there. Whoo case was not dry anymore There you go four out of eight LeBron James and that is a 14k solid gold or 12 no half-troy ounce of gold There you go So Dan T with the Lakers congratulations, man Yeah, I know right yeah, it is over insurance Jasper's case rates at Gmail Yeah, or click the support button. Yeah Well, there you go guys. Well, that definitely made up the case right there There you go There is Basley you got Dylan Miller RPA Alan Houston daughtery Tyron Lou Copey white base Oladipo Ben Simmons stainless stars pool Redemption the Andre Hunter Kelvin Johnson you go for that's gonna go to the Clippers Dave Cohen to 10 Wiggins one-on-one John Moran stainless stars to 99 Nola Jackson Hayes Redemption Nikolai Hustovic and the Alexander Walker for the Pelican Jalen Rose mark price Calvin Johnson Calvin Johnson Marcus all appreciate it guys. Jasper's case breaks calm


The next 7 Star Terrarium Event for Pokemon Scholar and Violet has just been announced, we're going to cover all of the details in today's video. So on the back of the 7 Star Typhlosion and Blissey Spotlight Terrarium Event's ending, we have had the announcement for our next 7 Star Terrarium Event and it comes as a big surprise. Hot off the press, Cerebi is on it as always. We've got the announcement that it will be Intellion, which will be the next 7 Star Terrarium Pokemon happening this coming Friday in Pokemon Scholar and Violet. It will have the Ice Terra typing tied to it, so a bit of a unique typing, something that we haven't seen before. Like I say, it will be running from April 28th until the 30th. That'll be the first phase of this event and then it'll be returning to our games from the 5th of May running through to the 7th. So we'll have two opportunities to battle this Pokemon, catch it. Of course, the details on this up to now are pretty sparse. We don't have much information. The Japanese website hasn't updated as of yet, but as we know from other 7 Star Terrarium Events, it will have the Mightiest Mark, it will be level 100, it will have the Ice Terra typing tied to it and you'll only be able to catch one of these per save file. So it's a pretty nice event, not one that I was expecting, like I say. We put a poll up on the channel at the start of the weekend asking you all what Pokemon you thought would be coming in the next 7 Star Terrarium. This was not one of the options, but another 8th generation start at joining the Scholar and Violet Pokédex, which is very exciting. Obviously, we've had Cinderace already now and Teleon joining the ranks and we are likely to get Rillaboom very soon. What starter Pokemon we'll get after that is anyone's best guess, but I'm hoping for things like Infernape and Polyon. Obviously, Blastoise, Venusaur would be really cool. If we get them, they're not on the game data, but I'm pretty sure that we will get those canisters start as at some point along the line. But what we'll get before we get home compatibility, of course, is anyone's best guess, like I've already mentioned and hopefully home does come soon, but we look like we're going to get a bunch of starters and these are coming thick and fast every single week. So this is the next one. Obviously, it will be coinciding with that Walking Wake and Iron Leaves Terrarium event that will be coming back for those players that have the issues with the bad egg from the latest 1.3 update, but the Intellion is going to be a lot of fun. Of course, we will be doing a best builds video for this later this week, going over the best Pokemon to help you prepare for this raid coming up. So do keep an eye out for that one. But a very quick update today just to let you know that this will be the next raid event that will be happening in our games later this week. If you found today's video useful, please drop a like. Do subscribe to the channel to stay up to date with all of our latest Pokemon scholar and violet content, as well as our best builds videos which go over some of the best options to go into these raids and help you beat them first time solo in your game or online. Thank you so much for tuning in friends. Let me know down in the comment section below what your thoughts are on Intellion, joining the ranks of Pokemon scholar and violet and I will see you all in another video very soon. So until then friends, take care of yourselves and bye bye.


So let me recall where we are. So we're on our way to prove versions of weak, strong, and let's call it the space-like singularity conjecture for the Einstein scalar field system under spherical symmetry. So just to make sure everyone's on the same page. So this is the system. This equation coupled with the scalar field with this energy momentum tensor. So the scalar field then satisfies the wave equation. OK? So under spherical symmetry, and I won't repeat everything that we've sort of said over the last times. But remember, always spherical symmetry is an evolutionary assumption. That's to say, you assume it on initial data and you get that the spacetime that evolves is very symmetric. Then in case the metric finally, it's very symmetric metric can be covered, as we said last time, globally in double null coordinates. So this is the form of the metric. And the Einstein equations coupled to the scalar field take this form. So these are the equations satisfied by the metric. The wave equation it takes, actually. You can write it in this form. And it's useful to point out, again, various things. These equations here are secretly the Reicherduri equation. And you notice immediately this monotonistic property. And the other thing to remember is this quantity here, the so-called Hawking mass. It's a very useful quantity in general in spherical symmetry. Particularly, it satisfies nice evolution equations, which I wrote down in their general form last time. And specialized to this system, the evolution equations look like this. And one thing that we showed last time, given the nature of our initial data, is that this Hawking mass is everywhere non-negative. So we showed that, if you remember. All right. So we ended the last time with a statement of this proposition. So the proposition is the following.  And there is a sequence of trap surfaces that approach this. And of course, a spherical symmetric trap surface, given, so maybe I should also remind you that we also showed, given our assumptions, that we always have this inequality, the u derivative of r, let me also just, that some of you might not, this might not be a completely second nature to everyone in the audience. So the d by du derivative goes this way, d by dv that way. So the d by du derivative of r is negative, we established that last time. So trap surface is equivalent to the statement that the d by dv derivative of r is negative. So suppose I have such a sequence. Then the Penner's diagram of spacetime is this. That's the claim. Moreover, the future null infinity is complete. So r equals 0 is a space-like boundary. So there are no null components of that. And we'll review this immediately. And moreover, the metric is inextendable beyond. Now, I put a star. This is actually a sort of a footnote. So in principle, you should be able to say that you are C0 inextendable beyond. But the most general sense in which you want to say that, strictly speaking, has not been actually shown. So that's another good exercise to try to do, to show that actually you are C0 inextendable. You are manifestly, I claim, C2 inextendable. But you can say certain stronger statements already, but the best statement that you might want to say is actually, strictly speaking, open. So with that footnote understood, then a corollary of this would be, if I can show that generically this happens, or I have the Penrose diagram of Mankowski space, of course, then all the conjectures, weak cosmic censorship, strong cosmic censorship, space-like singularity conjecture would fall. If I could show that generically this holds. Well, so let's show this. So it turns out that given what we already know, there are sort of three pieces of information that I'm telling you in this picture. So the first piece of information is sort of the easiest to understand. So I'm telling you that if you have a first singularity, so prove, so let P be a first singularity, not on gamma, so not this one. So the claim is that in general, what do I know? Since my mother model is tame, I know that the infimum of r in this rectangle is equal to 0. I know that this is preceded by some rectangle completely in the spacetime, and I know that the infimum of r is 0. So without a loss of generality, I claim that I can find the sequence of points which are in the interior of the rectangle, such that r goes to 0, such that the Pi is the sequence drawn, r goes to 0. OK, so now think about the following. Remember, this is a rectangle, which is completely in the spacetime, except for this point. So this is a compact set, which is completely in the spacetime, the lower two edges. So r has an infimum on these lower two edges, which is strictly positive. So here and here, r is bigger than some epsilon, which is bigger than 0. So what this means is that if you go very close here, so which I don't know, let me do this direction, because it's the non-trivial one. So if I go very close here, r was greater than equal to epsilon here, r is less than epsilon, if I'm very close, just on the sequence. So that means that on this no curve, somewhere in between, somewhere here, dv of r had to become negative. So dv of r had to become negative. But then what do we know from good old Raichadoury, from this equation here? We know that, again, remember, to re-prove what we know, you have to remember the covariance of the equation. We know that that's preserved. So to the future now of this point on this null cone, dv of r is less than 0, which means that r here is less than whatever r was there. So first of all, this tells us two things. So the first thing this tells us is the following. So suppose there is a null boundary component here that emerges from the first singularity. So I claim this immediately tells us that r would have to be equal to 0 on this boundary component. Because you see, I have a sequence now of these segments for which r is going to 0. But of course, du of r is always negative. So this tells me that monotonically r is going to 0 on all null curves that go in this direction. So that's clear. But remember now we know something else, which I advertised at the very last time. So this equation here, we can rewrite it as, let me get the sign of the factor right, we can rewrite it like this. And so in view of this, this also has a sign. So I'm telling you that asymptotically, this r difference is 0. But of course here, dv of r is strictly negative. So this r difference is strictly positive. This minus this is strictly positive. How are you able to say that? So easy exercise, this is now impossible. Because maybe I should say it like this. This minus this is strictly negative. In the limit, this minus that has to be less than equal to this minus this. So it cannot be that asymptotically, this minus this can become 0. So what we've just shown is there can be no component coming out like that. There does not exist. So the same argument allows you to say that first on an ingoing null component, r is equal to 0. In fact, this is easier because dv of r is always less than 0. And then that same inequality allows you to say that this is actually impossible. But note that we really, to show that r has to vanish here and there if there are such null components, that's actually quite general. We only really used Raichadoury. But to show that the components are absent, we use this extra monotonicity, which is special to the Einstein scalar field system. All right, that's great. So the second piece of information that I'm telling you in this proposition is that, so what I'm telling you is that, OK, let's, so where are we, maybe, I should say? That's to say, what is the most general picture that we could have? So of course, under our assumption, I know that the past, the future null infinity, has non-empty complement, because I have at least one trapped surface.  I just told you that the first singularities form a space-like boundary. There are no null components emanating from first singularities. But you can still have null pieces here, and you can still have a null piece there, of which so far I've told you nothing. So let's look near here. So suppose you have a null piece here. Is this possible? So let's just think about it a little bit. So suppose you have a null piece of the boundary here, which is in general allowed by what we've proven so far. And here we're going to use the assumption, namely that we have this sequence. So this is a sequence of trapped surfaces. So dv of r is less than 0 on this sequence, and the sequence converges there. So claim, by the way, without loss of generality, I can put the sequence here. So if the sequence was there, a little exercise using Raishaduri, construct the sequence, which is on this side of that null column, that would be more useful for me. All right, so what did we say? So first of all, what is the r value of these trapped surfaces? I claim to you that r goes to 0 as you go along the sequence. Now you might think that's obvious, because r is 0 here, but of course, no one tells you that r extends in any way continuous to this a priori. So why does r go to 0? And here, we can use our good friend, right. So I want to use our good friend monotonistic, but actually, it's a two-step process. So let's do the two steps. So first of all, if this is the case, you can first go sort of to the past along these, all right, such that you reach the, you know. So you see, OK, this is a trapped surface, but this is an open condition. So there are trapped surfaces earlier. So there are trapped surfaces earlier. So I want to find a marginally trapped surface, so a surface where dv of r is equal to 0. And with the property that if then I go earlier, dv of r is greater than equal to 0. So maybe I'll draw a slightly bigger picture to make this clear. So the claim is the following. At the center, r is equal to 0. And remember, r is greater than 0 everywhere in the bulk. So certainly, as you come off the center, dv of r is greater than 0. So if I know that, let's say, on this null curve, there is a trapped surface, then there is a first surface where dv r is equal to 0. So let me look first at these surfaces. And now I should, I guess, say that this sequence, you don't know if it's on this side or on that side. So it could oscillate. Doesn't matter. So this is a sequence such that dv of r is equal to 0. I don't like this picture. So I claim that actually, I can say something better than this. Namely, I can say that this has to be the picture. So why did this sequence, again, have to be sort of on this side? Well, it's, again, this relation here. So if you are the first, so if you have the property that dv of r is less than equal to 0 here, then, well, certainly, that has to be true from then on by this.  So actually, this sequence is, again, here. And it looks like this. That's to say, if I look at a later thing in the sequence and I go backwards, then dv of r is greater than 0. All right. So now, finally, I can tell you that on this sequence r goes to 0, from which it will follow that on my initial sequence of trapped surfaces r goes to 0. Because, of course, if this is the first marginally trapped surface, then dv of r is less than equal to 0 here. And so r here is even less than r there. So to recap, I know that the sequence of, I have a sequence of first marginally trapped surfaces. First in the sense I said, such that dv of r equals 0. And I want to show that r goes to 0. So I claim that this is clear, simply from the following statement. So let's look at this r difference. And compare it to this r difference. So over here, dv of r is greater than equal to 0, from here to here. On the other hand, du dv of r is less than equal to 0. So that tells you that this r difference is less than equal to this r difference. All right, but now if you think about the geometry of this, this point is too big. So this point is converging there. So if I draw these rectangles for later, later points, they look like this. So this r difference is always less than equal to that r difference. But that r difference goes to 0, because the dimension of the rectangle here is going to 0, and the data here is regular. So that's actually immediate from this nice one. So to recap, what I've just shown you is that on this sequence of trapped surfaces, which again are on this side of that backwards null cone coming from this point, r is going to 0. Well now, OK, I claim that immediately I know that if there is a null piece coming out from there, r better be 0 identically here. Well, why is that the case? Well, again, I know that r here is very small. And if I go on the outgoing null cone coming from there, dv of r is less than 0. So r is even smaller than what it is here. So I have now these null curves. And on this whole null curve, r is smaller than something which is tending to 0, as I put the point there. On the other hand, again, r is monotonically decreasing in this direction. So indeed, r has to be 0. But now the exact same argument that we used to say that you could not have these null segments tells you that, so in fact, this is a contradiction. Again, you're contradicting always this. So that's great. So finally, what this is telling you is that if I have this sequence, then the r equals 0, I have to have a curve of first singularities that goes into this point. OK, so the last issue, and this is in some sense the one that we actually have to use some more information that I haven't told you yet, is how do I know that I do not have a null piece coming from there? And this will be interesting exactly because this property is the property that won't be true in greater generality. So what can I say here? So here's the point. So remember, I've already told you a few extra things about what happens in this situation. So let's sort of assume for sake of contradiction that near this point, the Penrose diagram looks like this. So what have I already told you? I've already told you, yes. Say again, sorry? The sequence of first singularities is somewhere over there. I haven't depicted it. So the claim is the following, that the existence of the sequence is just telling me I'm just using it here. So for this part, if you want, all I need, all I am using is the existence of one trapped surface, just one, because that's what's telling me that the future of null infinity indeed has a non-trivial. It's passed as a non-trivial complement. So I now want to look at near this point and exclude this possibility. This one? This one? Oh, yeah, I don't know what this was supposed to be. Nothing. This was the sequence. There's no claim that this sequence has anything to do with this point.  It's a completely, quote, local statement near this point. I'm going to say, you know, you cannot have this Penrose diagram near this point. So let's do this. So what other information do I know? Well, I know this Penrose inequality. That's to say, I know that r goes to some r plus along here, which is less than infinity. OK? Let's see what I can get just from knowing that. So I claim to you that, so this is sort of a funny little exercise, so I claim to you that you can already show the following. So of course, all right. So I can talk about the limit of r on this boundary, where by limit I just mean the limit in this direction. So why can I talk about that? Remember, r is almost monotonic in this direction. Its derivative can change sign exactly once, which means that eventually it is monotonic. So I can certainly talk about the limit of r here. So I can talk about r there. So let me affirm the following statement that actually r, whatever it is, has to tend to r plus as you go this way. So this is sort of a nice little exercise. So suppose it doesn't. Well, it certainly cannot tend to something bigger than r plus. I claim that you can easily see contradicts the fact that the u of r is less than 0. That's a very easy argument.  Then you could find a sequence of points like this where, I don't know, r equals r plus minus epsilon over 2, and r equals r plus minus, I don't know. Maybe let me make this minus, I need a number of epsilon over 4, that's fine. You like that? So in particular, so that's sort of an easy exercise. And the sequence of points have the, I claim you can choose them, so that this point is lying on this null curve, backwards null curve coming from there. And now you can sort of throw away a bunch of these points, so you can always wait in the sequence such that the next one of these points has a lower u value than this point. So you can find the sequence of points of if you want intervals like this, and these intervals go there. All right, this is my favorite way of saying this, just because, so what is the r difference here? r difference is epsilon over 4, right? But now I want to use this relation, but I'm going to use it in the other direction, trivial fact analysis. So what this is telling you is that if you go at a later time, I just don't have so much, then the r difference is at least the sum of these. But there are infinitely many, so you'd get an infinite r difference, which is a contradiction. So I let you think about this picture, but the claim is that this is immediately contradicted by this monotonous. So you actually have this. So that's great, but we haven't yet disproved anything. So you could have this, right? So I have to tell you some more information, which is actually more difficult to show, but you can show it. So it turns out that by really using now the wave equation and its decay properties in the exterior, one can show two things about the exterior that will be important. So the first thing is that the event horizon is complete. I've never yet told you that the event horizon is complete. I've told you that null infinity is complete, but I've never told you that the event horizon is complete. What that just means is that this on the event horizon, let's call the event horizon u equals u0, is equal to infinity, so fact. Again, this fact depends on the analysis of waves in black hole exteriors, something that's been a subject of much research for some time. So this is one thing. But I'll give you another fact. So fact two is that if I look at the integral of dv phi in absolute value along the event horizon, dv, this is finite. Now, can you see the statement? Maybe you can. So yeah, it's a little bit funny. What's nice, so this is some sort of, this is a statement of decay for phi along the event horizon. And I claim this statement is invariant to the normalization of null coordinates. So if I rescale the coordinate v because I'm taking dv here, this is actually, so this is an invariant quantity. So let me tell you one third fact. So these are, if you want, difficult facts. But the third fact is actually immediate from the sort of monotonistic properties of m. Because I know that there is at least one trapped surface, then I know that m is strictly positive near here. In fact, I know that m is greater than some epsilon in some region like this.  And then you can follow the monotonicity of m like this. So I know that there's at least one trapped surface. That's all I need to be able to give you that. So all right, well, how can we argue from this point on? OK, so because I don't want to spend infinite time on this, I'll leave the various statements as exercises. But they're quite easy to do. I'll say it in words. And you can try to fill in the details. So the first thing you immediately notice is the following. I can look at that shaded region, that purported characteristic rectangle that supposedly exists here. Look at the shaded region. I can integrate this equation twice because of the finiteness of r. The left-hand side of this is bounded. It's just the r difference of two endpoints of the rectangle. So it's bounded, whatever it is. r itself is bounded below, away from 0, m is finite. r is bounded above, maybe that's more pertinent, by r plus in that region, again, by the d ur less than 0 monotonicity. So it follows that the double integral of omega squared is finite. So similarly, if you want the double integral of r squared omega squared is finite because r is bounded. So that's actually the spacetime volume. So just a remark. So if I'm in the situation, then the spacetime volume of this is bounded. So now let's look at this equation here. And let's integrate it twice. So it's maybe most convenient to, at this point, choose a particular normalization of the v-coordinate. So I'm going to use, this is not necessary, but it's sort of makes me feel better. I'm going to use a normalization of the v-coordinate such that omega squared is equal to 1 on the event horizon. And of course, because I just told you that the integral of omega squared is infinite, that means that this will not be a bounded v-coordinate. But nonetheless, I'll draw it like this. So this is the event horizon. And of course, this will now be v equals infinity. And omega squared is equal to 1 here. And again, imagine I have this sort of rectangle. I can translate the coordinates so that the edge of the rectangle is, let's say, v equals 0. It doesn't matter. So let me try to integrate the equation store in this region. So here's the point. I'm also going to really consider a very, very small region. So that whatever omega is here, it's very near 1. In fact, if you want, for convenience, let me rescale the u-coordinate here such that omega squared is equal to 1. So if I integrate this equation twice, as far as the left hand side is concerned, I have no initial data terms because the log of omega is initially 1. So I'm just going to get the log of omega, let's say here, and some double integral here. So what's the double integral? It's the double integral of this, of this, and of this. So I just told you that this double integral is bounded. It's finite. It's something. So it's uniformly bounded, no matter which point I take. So what about this double integral? I claim that it's also bounded. Maybe the easiest way of seeing that is putting this term here on the left hand side and integrating this again twice over u and v. So you get then that this double integral is bounded. And OK, they only differ by the different weights of r. But r is bounded above and below. So the last thing that you have to understand is this double integral, this double integral. And it's a very nice exercise, I think. It's not a difficult exercise to show the following. So given this assumption here, I know that if I put my v equals 0, very, very late, the integral of dv of v is finite. It's fact I can even make it small initially by choosing this time to be very late. And again, by choosing this sort of rectangle to be very short, I can certainly just by regularity, ensure that this integral, the integral of du phi in norm, is less than epsilon. So then you look at the wave equation. This is the wave equation. And I've written it in this form. And when you write it in this form, it's very nice because you don't see omega at all. You just see r. So somehow, here is my exercise for you, integrating in a smart way the wave equation, using the fact that the r difference in this rectangle, so what I'll call r minus r, r of x minus r of y, for any two points, is less than epsilon if I make the rectangle small enough. You can show that this double integral is also bounded. And now I claim this is a contradiction because what you've shown is you've shown that log of omega in absolute value is uniformly bounded in this whole region everywhere. But that means that omega is like 1. Log of omega is uniformly bounded. It means omega is like 1. It's bounded away from 0, which means that the integral of omega squared is like the integral of 1 du dv. But the range of the v coordinates is infinite. So it's a contradiction. OK. So anyway, that's the proof of that. Exercise, fill in the details, or maybe find a simpler arc. So now, we've completed this proposition. So now let me tell you the actual meat of Chris D'Aulou's work for this model, which is precisely the statement that, generically, we are in the domain of that proposition. So this is the theorem. Actually, it's good that there's some musical accompaniment. All right. So the statement is for generic initial data, and I'll get back to this in just a second, then if there exists a first singularity on the center. So remember, if there does not exist a first singularity in the center by what we said previously, the Penrose diagram is that of Minkowski's space. And again, everything is true. So if there exists a first singularity in the center, then it's accompanied by such a sequence, then there exists a sequence. So there exists a sequence of trapped surfaces, as in the proposition. So corollary, weak cosmic censorship, strong cosmic censorship, well, certainly the C2 version. But as I said, that's not the right version. In principle, the C0 version. Maybe it's relatively easy to show a slightly weaker notion of the C0 version. Namely, you cannot extend C0 as a spherically symmetric space time. But in any case, I just put the asterisk that there's a nice little exercise to complete here. And the space-like singularity conjecture, true for Einstein's scalar field in spherical symmetry. So that's his steer. So let me just discuss a little bit the proof. Because somehow the proof is much more subtle than anything we've done on the board so far. And so I really can't give it justice, but I can tell you the mechanism, which is very pretty and relatively easy to describe.  So the first, if you want, thing that he shows is the following. If you have this first singularity on the center, then something has to go wrong at this first singularity. But what has to go wrong? Remember, we got a load of mileage for first singularities outside of the center saying that R had to go to 0. In fact, we're using this all the time. Of course, here that R goes to 0, you know it. Because you're on the center, and so R is 0 here. So how can you characterize what goes wrong here? So first of all, he is able to show the following that 2m over R, so this is in some sense a dimensionless quantity, this has to be bigger than some sort of universal constant in this model, which is strictly positive. So the limit, and let me not say precisely what I mean in what sense the limit, but particular there has to be a sequence of points, such that this quantity here is strictly positive in the limit, in fact, bigger than some particular constant that you can actually compute. So this is sort of claim 1. And this is already actually quite difficult to prove. We're very nice to have sort of analogous statements for other mother models. There really is not anything available like this. So that's the first statement. So now I'm going to rewrite this equation here in yet another way. I'm going to write it, so sort of looking at this expression and recalling the definition of m. I can rewrite this expression. Let me write it correctly. With the right sign, I'll get the sign wrong. I'll get the 2m over R. So all I've done, you can see it from this form here. All I've done is I've solved this equation for omega squared and plugged it in there. OK? So again, I'm going to, what am I going to do now? I'm going to think of this as an evolution equation for dv of R on the backwards null cone emanating from this first singularity. So this equation is telling me du dvR is equal to something and I think of it as an evolution equation for this. And I try to integrate this equation as a linear equation in dv of R. So here's the point. Because I know that this is true in the limit, I can rewrite this as 1 over R times something bounded below away from 0. And then this, if you want, without loss of, I mean, by the argument that we already saw actually, I know that this is greater than, I mean, this expression here is less than 1. So this is a factor that only makes things bigger. And I can integrate this duR. So what does that tell you? It tells you the following. Since R is going to 0, the integral of this diverges. So that's telling you that the quantity dvR is becoming 0 because you have to also remember the sign. So dvR is becoming 0 as you go over there. So what does this mean? So I claim that this is a blue shift effect. Because this means that if you have two observers here and here, and the observer normalizes their time to R, which is the only canonical thing to do, then the observer here will see radiation coming from here as infinitely blue shifted. So that's something you can think about very easily. Now in this model, you have radiation sitting around because you have phi. And what you want to show now is that generically, that blue shift tends to concentrate energy between, where is a good picture, between here and any close enough point like this to make this trapped. So that's basically what he shows. In fact, what he shows is that if you happen to have a solution such that there were no trapped surfaces that went there, then by adding arbitrarily small perturbation, in some sense, which lives here, then this blue shift effect forces the existence of those trapped surfaces. So that's essentially what he shows. Now one interesting thing about the argument is that in order to exploit this, it's very useful to allow the initial data to be slightly irregular. That's to say to always consider initial data that are not smooth, see infinity, but slightly irregular. Slightly irregular but still in the class of a well-posed theory. So part of the difficulty is identifying such a class that gives you the flexibility to be able to carry out this argument. So he also sort of discovered, so class refers to the function space defining the initial data. And the second interesting thing to point out in this context is the generosity is necessary. And so this is necessary. I want to stress this was not thought to be the case before. I already mentioned that in the context of the dust model, weak cosmic censorship is actually violated generically within the context of spherical symmetry. But in that case, it really is because of a failure of the model. The Einstein scalar field system is as good as it gets as far as models are concerned. The Mather equation is completely linear, so there's nothing wrong about the Mather. The Mather certainly does not form singularities on its own accord. So the original hope was that there would never be naked singularities in this model. And so in parallel with this proof, he actually constructed examples where the Penrose diagram looks like this or like this. So there are examples, OK, spherical symmetric examples that look like this, but they are not generic. So the theorem tells you that they are not generic. So in particular, these examples were you to perturb them, you would have the Penrose diagram that is drawn over there. OK. So that's Kriste Zoulou's work. So this is great. I have 20 minutes. And in 20 minutes, I will give an abridged version of lecture four, but in some sense, I think that's exactly the amount of time that we need for it. OK. So let me write here, maybe. I warned you at the beginning, of course, that I'm not going to keep to my schedule. OK. So lecture four, the C0 stability of She-Heroisen without symmetry. Without symmetry. OK. So before I say anything about Kr, let me say something far more elementary, OK? Let me say something about Reisen and Nordstrom, OK? So I've already drawn in a previous lecture the Penrose diagram of Reisen and Nordstrom solution. So let me draw it again. So remember, Reisen and Nordstrom is a solution of the Einstein Maxwell equation, so Timini is, OK. So exercise, adorn this with indices so that that is the correct energy momentum tensor for a Maxwell field, OK? And then the Maxwell equations, of course, are just that without any mother, which is charged, are just this, right? So Reisen and Nordstrom is a spherical symmetric solution of that, OK? It has two ends, and its Penrose diagram as defined in the sort of notations of this course looks like this, OK? And this boundary is actually completely regular, so I can extend the solution here, move the extents, and of course, any such extension is manifestly non-unique, OK? So let's just focus on this rectangle. Let's just focus on this rectangle, OK? So if I focus on this rectangle, then, OK, the global aspects, the fact that I have two ends, et cetera, it's really irrelevant, OK? What is going on in this rectangle that's different from before? Because before I gave you an argument in the Einstein-Scaler field model that you could not have this behavior. So what's the difference? Well, OK, I'm going to, OK. Sorry, but we like graffiti a lot in Greece, so I'm going to do some graffiti. So let's understand the extra terms that you would have in the Maxwell case. So I claim that actually, even though this is a lot of equations to write down, in spherical symmetry, the Maxwell part is not dynamic. So it just gives you a constant times something depending on the metric, which appears in the equations. So we call that constant 2 squared. So I have an extra term here, which looks like this. And I have an extra term here also that looks like this. So if you won't forget about the scalar field, there's no scalar field now, bye-bye scalar field, but you have q, these are the equations that Reisen and Nordstrom satisfies. So actually, exercise, understand completely the Penrose diagram of Reisen and Nordstrom just from the equations without writing down the metric explicitly. It's actually an illuminating exercise. So in particular, I claim to you that the reason that this can now happen is because of this term. So in particular, you lose the very nice monotonicity that DUDV has assigned.  And it's this term here, let's say in this equation, that is driving the phenol. So the first thing you might ask is whether in spherical symmetry, having Cauchy horizon is stable. And somehow the easiest model to look at that is the model where I just couple both the scalar field and the Maxwell, but I don't even bother to make the scalar field charged. So this is a model. It admits Reisen and Nordstrom as an explicit solution. Unfortunately, Reisen and Nordstrom is the only spherically symmetric electro-vacuum solution. So if you want dynamics in spherical symmetry, you have to add matter. So let's just add the scalar field. But let's not even make it charged. So this is the energy momentum tensor. So you still have the wave equation. You have these equations. And just that you still also have this term. So I should note that there are extra terms on these equations here. These equations are deduced from these. So a while ago, I showed that when you consider general solutions of these equations. By the way, in these equations, if you want q to be non-zero, so if you don't want these to reduce to Christodoulou's model, initial data has to have two n's. It has to have two n's. That's another nice, easy exercise. So initial data has to have two n's. And another very, very easy exercise is the following. Any time you have a tamed matter model, and this model is, again, tamed in the sense that we said, and you have two-ended initial data, then weak cosmic censorship is true, sort of trivially. And that just has to do with the fact that there's no center for first singularities to come from. So all the first singularities have to have r equals 0. And if you think about Richard Dury, you have that statement. So in this case, you always have weak cosmic censorship. You always have complete, future non-infinity. And the statement is the following. So if q is not equal to 0, there will always be null pieces of the boundary that come from here, which are non-empty. So this is something that I proved a while back. It also uses a study I did jointly with Rodnianski about the decay of waves in the exterior, because you really need to know rather precise information about the stability of the exterior regions here, and particularly the behavior of fields on the event horizon in order to say that this is the case. So in general, you may also have a space-like singularity here, although actually strictly speaking, in this model, the argument that says that the r equals 0 first singularities form a space-like singularity does not hold because of the failure of that monotonistic, duv r less than equal to 0. But in any case, the rest of the boundary, you can show that r is equal to 0. But actually, what I showed moreover is that if your initial data was close to Reissner-Nordstrom initial data, then there will be no such piece. And these will close off the space-like singularity. What I showed is that you can still extend this C0. So the metric extends. So in particular, in this model in spherical symmetry, the C0 extendability, inextendability formulation strong cosmic censorship is false in this model in spherical symmetry. Now, even though, so from the point of view of C0, this is a Cauchy horizon. This is regular. There's no problem whatsoever. But from the point of view of higher regularity, generically, there is a problem. And I had some partial result on that, but I couldn't quite get the full result. And actually, much more recently, Luke and Oh have shown that for generic initial data, the boundary is entirely singular. So they have a condition on initial data, which is a generosity condition. So for somehow, you should think with probability one, they have a precise statement in their paper. Then the boundary is entirely singular. And OK, they can say in particular that you are C2 inextendable. And again, the proof morally suggests that you have actually a stronger statement, maybe even a statement at the level of H1 in extendability, which is a formulation of strong cosmic censorship due to Stodulu. But there's still a little thing to complete in order to be able to say that. But in any case, you have a weaker formulation of strong cosmic censorship is true in this model in spherical symmetry. Now, in this spherical symmetric world, there's still nice things you might want to consider. So the reason that you need to have two-ended data here is because the scalar field itself is uncharged. So this Q, to be known as 0, has to sit on some topology. So this is the topology, right? You can consider one-ended collapse in this model by making, for instance, the scalar field charged. And actually, this model has been considered recently by Maxime van der Mortel. And he's been able to show a version of the stability of a piece of the Cauchy horizon. But under assumptions on the behavior of the event horizon, and actually, those assumptions are thought to be true always. But it's still much more difficult, even in that model, to retrieve those assumptions from assumptions of the level of initial data. So even in spherical symmetry, there are nice things to do. OK. In the last five minutes, I can state this result, which, in some sense, is the conclusion of the story of the C0 formulation of strong quantum censorship. So you might say, this is all very well. But at the end of the day, this is a spherical symmetric model. And what is generic within spherical symmetry may be completely un-generic outside the spherical symmetry, because spherical symmetry itself is measure 0 in the sort of probability 0, I'll have to say it, for general initial dot. OK. So is this really relevant more generally? So here's our theorem with, so I'll erase these equations now, with Jonathan Luke. This is a theorem released a few years ago now on the archive. So let me say it as follows. So theorem, so there are two statements maybe I'll make. So I'll make, in some sense, what's in some sense first the more general statement. So the more general statement is the following. So let's forget about symmetry completely. Since we're forgetting about symmetry, let's also forget about matter. Because in some sense, the motivation for the matter that we've been considering is exactly, we had to add matter to evade Perkov's theorem to have non-trivial dynamics in spherical symmetry. But somehow the conceptual question of cosmic censorship, after all, is first and foremost a question already about the vacuum equations. So vacuum, but now no symmetry whatsoever.   And I assume that, OK, the horizon, who knows what happens at early times, how it didn't exist. I mean, whatever, how it formed in the spacetime, however you want to say that. But suppose that at late times it settles down to Kerr. And it settles down at the expected inverse polynomial rates that it is believed that perturbations on event horizons decay in the very late time regime where they're governed by tails. So let's assume that your geometry settles down on the event horizon to Kerr. So it is actually believed that generic vacuum spacetimes will eventually either disperse or settle down to a finite number of Kerr's moving far away from each other. So we are now talking about, let's say, the neighborhood of one of them. OK. So suppose this is what you know about the event horizon. Then the statement is settles down to Kerr asymptotically. So let me write here this is sort of with Jonathan Luke. So the statement is then, well, of course, this is a spacetime without any symmetries. So I cannot define Penrose diagrams in the way I did. But actually, the claim is that the future of the event horizon and, let's say, an ingoing null cone can actually be covered by double null coordinates. You are not strictly symmetric, but you are still covered with double null coordinates. So I can, again, draw the range of those coordinates. And the statement is that the spacetime exists in a region that contains a characteristic rectangle in double null coordinates that looks like this. And in particular, this is a Cauchy horizon beyond which the spacetime is extendable. So what this tells you is if you believe sort of the completely standard picture of gravitational collapse for the vacuum, then the generic spacetime either disperses or will have a piece of Cauchy horizon across which the solution is extendable C0. And remember, extendable C0 means, morally speaking, that the observers, they are not destroyed. So they reach the Cauchy horizon without being destroyed. So an amplification, but also specialization of this statement is the following. So suppose, in particular, that you start here with initial data, which is globally near two-ended Kerr initial data for the Einstein vacuum equations without any symmetry. So it is believed that now, OK, this is more than a belief, sort of all the ideas necessary to prove rigorously, the fact that the exterior regions of the Kerr spacetime are stable and the solution will settle down to two nearby Kerr solutions. So this is what's sometimes called the nonlinear stability of Kerr problem, all right? So this is something that now can be shown, sort of putting together a lot of things. I mean, can be shown it's difficult to write something which is self-contained and readable, but in principle, this is now mostly a technical problem. So in particular, in this case, you will be everywhere close to Kerr, and you will settle down inverse polynomially to two nearby Kerrs. So in this case, while the theorem already tells you that, OK, near these event horizons from these points in the Penrose diagram, whatever this means now in this context, you'll have a little piece of Cauchy horizon. And actually, in this case, you can say something more. The entire bifurcate Cauchy horizon of Kerr is stable, and you can, in fact, extend the spacetime across the entire bifurcate horizon so that all observers that were incomplete in the original spacetime pass safely to the extension. C0. So somehow, not only in exact Kerr, but in small perturbations of Kerr initial data, it's exactly the same phenomenon that the spacetime, its Penrose diagram, is bounded by a globally null surface across which the metric is extended. So in any case, corollary of this already, so this would be an open set in the modular space of initial data for which the predicate of the inextendability statement that strong cosmic censorship wanted in its C0 formulation is false. So corollary of this is already C0 formulation of strong cosmic censorship is false. And this is a definitive statement. It is false for the vacuum Einstein equations without any symmetry. Now, again, just like with the spherical symmetric case and the work of Luke and O, it is thought that, generically, this boundary still will be singular in a weaker sense. And there are now many methods that have been developed to be able to show that, at least in a neighborhood of Kerr. So in particular, what that would mean is that, in a neighborhood of Kerr, some weaker formulations of strong cosmic censorship should be true and should be provable. Now, just remember one thing. To disprove a version of strong cosmic censorship, it's sufficient to find one open set in the modular space of solutions without symmetry of what you understand, one truly open set for which the statement is false. To prove a version of strong cosmic censorship, weak cosmic, whatever your favorite thing, then, OK, this is something about the whole modular space or generic in the modular space. So a complete proof of some formulation of strong cosmic censorship that may be true still looks like it is very, very far off. But a complete resolution of the picture in a neighborhood of Kerr is now very much within reach. All right, let me end there. Thanks a lot. Thank you.