Thursday, March 13, 2014

Galactic gravitational fields b

Be sure to see the primary article in this series at

 Galactic gravitational fields

Gary Kentgen[1]


The set of gravitational fields postulated herein centers around supermassive black holes of the kind seen at the centers of spiral galaxies. The concept is not limited to such particular supermassive black holes because all black holes should display these 2-D hyperbolic (1/r) and hyperparabolic (1/r3) gravitational field “surfaces” embedded in 3-D + t spacetime. It is necessary to postulate a full set of gravitational fields based on unique properties of black holes. A single type of field does not work in descriptions of our universe. But allowing more than one type of field solves many vexing problems such as the anomalous velocity dispersion of stars in galaxies and of galaxies in clusters and even the Bullet Cluster effect. Using the hyperbolic (1/r) supermassive black hole galactic gravitational field, one can even derive the MOND acceleration constant, ao.


The small set of gravitational field types postulated herein centers around supermassive black holes (SMBH)s of the sort seen at the centers of spiral galaxies. And, allowing more than one type of field solves many vexing problems such as the anomalous velocity dispersion (AVD) of stars in galaxies and of galaxies in clusters[2], the Sunyaev Zel’dovich, the integrated Sachs Wolfe and the Bullet Cluster effects. Also, the hyperbolic (1/r) central SMBH gravitational field will help explain the temperature distributions across galaxies and the pattern of variations in the CMB[3] (because they are consistent with the values that were previously determined).

Embedded in 3-D plus t spacetime, the galactic 2-D Hyperbolic (1/r) Gravitational Field (HGF) complex surface-like shape is a hyperboloid of one sheet[4] (at very large r). Significantly more (or less – when gravity declines as 1/r3 therein[a]) intense long range fields embedded in 3‑D spacetime allow the hyperbolic fields of nearby galaxy central SMBHs to interact preferentially to form a complex network or 3-D array. Helping to evolve large scale structure[5], this also would allow creation of a facsimile of “Dark Matter” (DM) halos around galaxies and clusters so that it would account for all the phenomena attributed to DM, including the AVD.

In a very rapidly spinning black hole where mass-energy has collapsed to a virtual singularity[6] beneath the event horizon[7], only the z dimension has shrunk, according to the Postulate. Because all mass-energy entering a black hole must initially have a nonzero, effectively co ‑ moving orbital velocity component, all such material must orbit at faster and faster speeds which advance toward infinity as the orbital radius shrinks[8] and the singularity is approached. Net orbital and rotational radii must shrink due to chaotic interactions and/or simple gravitational effects. “Orbital friction”, mutual tidal effects and even relativistic properties may also play a large role. 

Such in-falling material must orbit in concert[9]. That is, initially, it all must orbit in roughly the same direction so that as its orbital radius shrinks the BH can be thought of as if it was rotating faster and faster as a whole. As it shrinks due to “orbital friction”, chaotic interaction and relativistic effects, it acts more and more like a single rotating body. Then, rotating faster than c below the event horizon, the nature of spacetime itself must transform. It undergoes a centripetal “phase change”[10].

It forms a flattened disk of nominally infinite radius. This spacetime matter-gravitational field disk can ignore the event horizon (EH). While its mass is still constrained by the EH, the field is not so limited because it is a spacetime entity[11]. The shapes of a whole set of hyperbolic gravitational fields is depicted in Figure 1 below.

Collapse in the z dimension of the galactic central SMBH means that mass‑energy‑spacetime (MES) becomes unified in a new way. It forms, not a ring singularity á la Kerr, but an indefinitely broad disk singularity that is singular only in the z direction and nominally infinite in the x, y directions due to centripetal and deeply hyper-extended pure relativistic frame dragging effects[12] available to it in 2-D. So, this MES entity still exerts a far reaching 2-D gravitational field because the spacetime component of its nature can ignore the event horizon while retaining all its mass below it.

Relativity theory unites matter, energy, space and time via  E  =  mc2. This black hole behavior only confirms Einstein, Schwarzchild and Kretschmann. It indicates that Einstein’s theory may be UV complete and may require no revision, update or replacement.

Depiction of how a network might arise

Figure 1 is meant to depict how a network might arise from the hyperboloids of one sheet[b] that would exist surrounding supermassive central BHs in galaxies.  Actually, in Fig. 1, the gravitational fields of each SMBH putatively extend to infinity except whenever a hyperboloid surface of one SMBH meets a surface of another SMBH almost head-on. Then they form a preferred gravitational link between galaxies because gravity in this space between central SMBHs declines only as 1/r. Since these Fig. 1 hyperboloids are viewed from a cosmological perspective, they appear quite pinched at their centers. But, of course, in fact they are. This network will become exceedingly complex if clusters or superclusters collide.

The part of a hyperboloid that is not enclosed within the hyperbolic quasi-surface itself, the cages or baskets and the circum-hole groove are an “antihyperboloid” of spacetime which is postulated here to gravitationally decline within it as 1/r3, perhaps as a separate quantum-like “state” of the black hole. It might be called a “hyperparaboloid”.


Figure 1

The edges of the hyperboloids are to be extended indefinitely, not truncated like this. The surfaces are depicted like this for convenience.

The faster decline of G with r in these galactic SMBH hyperparabolic (1/r3) spacetime regions of 3-D spacetime are not gravitationally neutral or maybe not even slightly repulsive so that the network that forms along with the hyperbolic (1/r) contribution has an “open cell” or sponge-like structure. Gravitational hyperparabolic (1/r3) spacetime in conjunction with SMBHs is also permitted by general relativity[13],[14],[15]. It helps reinforce the open cell lattice‑like structure of the matrix of galactic superclusters.

Ordinary inverse square (1/r2) gravity around a galactic central SMBH, being omnidirectional in nature, cannot produce this kind of structure. But, the highly directional hyperbolic (1/r) sheet of a central SMBH can do so.


Figure 2

Large scale structure of the universe

Objections to all this

One might object to all this on the basis of Birkhoff’s[16] and the “no-hair”[17] theorems and even Newton’s law of universal gravitation itself[18]. The no-hair theorem is not a mathematical theorem at all. It is a postulate, a tentative assumption that ideal black hole solutions of the Einstein equations of gravitation in general relativity can be completely characterized by three externally observable classical parameters. These are mass, electric charge, and angular momentum (spin).

Other information (nicknamed "hair”) about matter which entered a black hole "disappears" behind the black hole event horizon. Supposedly, it is therefore inaccessible to external observers. John Archibald Wheeler enunciated this idea as "black holes have no hair", the source of the name. But, it is now accepted that no information is lost in the formation of BHs[19]. The HSMBH gravitational field can exist, hair or no hair.

Newton’s law is sidestepped by postulating a black hole gravitational field that has different dimensionality in cosmologically scaled space. On cosmological scales, unusual things should be possible.

With no strict mathematical proof of the so called no-hair theorem, mathematicians rightly refer to it as the no-hair conjecture[20]. Even in the simplest case of BHs with intense gravity alone (that is, zero electric fields, no spin), this conjecture has been only partially supported by results of research to date.

Researchers have been working under the additional hypotheses of simple event horizons and difficult to justify assumptions concerning details of the mathematical and physical reality of spacetime near black holes. Birkhoff’s theorem does not apply because of the unrealistically simple conditions he requires. Kerr’s[21] and other’s treatments are almost equally simplistic. In other words, there is no theoretical constraint, including from relativity theory, that would obviate the central galactic, hyperbolic (1/r), supermassive black hole, spin induced gravitational field.

Bending of background illumination by galaxies and galactic central SMBHs

The ultra-high-spin induced hyperbolic (1/r) central galactic SMBH spacetime parcel is composed of a spacetime continuum segment or relativistic parcel that can behave as if it had a refractive index  >1 relative to ordinary gravity-free 3-D spacetime. So, no matter what pathway is traversed through the parcel by a ray of light, the 2-D HSMBH gravitational spacetime packet can bend the trajectory of electromagnetic radiation, as depicted in Fig. 2.

Figure 3
Derived from Fig.1, this depicts how illumination from behind might interact with the gravitational fields of a cluster of supermassive black holes.Regardless of the pathway through a galaxy cluster, light is bent by the hyperboloids, even when the ray passes perpendicular through the thin part of a disk.  The hyperbolic (1/r) gravitational fields act like connected parcels of spacetime having a refractive index > 1.  The reverse Compton effect acting on the ray is permanent. The redshift process itself is ongoing. 
Mass estimates based on gravitational microlensing suggest that the hyperbolic (1/r)gravitational masses of SMBHs should be combined or added to the inverse square (1/r2) galaxy masses unless these masses are recomputed via the Postulate. Such a recalculation would be preferred. We think that SMBHs should have masses comparable to galaxies (on the order of 1011 solar masses). We will attend to this more fully in a future paper (see ref. 21).

For modeling purposes, each galactic SMBH can be considered like a polyfunctional monomer from which will be constructed a crosslinked polymer. For crosslinking, such a monomer must have more than 2 functional groups to which other monomers may attach. The two lobed hyperbolic one‑sheet is ideal for this. A variety of orientations and attachment points are permitted for conjoining numerous galactic SMBHs.  Viewed as a whole, such a polymer will appear to have random orientations of its SMBH monomers. Its structure would look like the cobweb or sponge-like pattern such as that seen in diagrams derived from the Sloan Digital Sky Survey results in Fig. 2[22], [23].

By the way, one wonders whether the universe may be considered to be actually composed of a medium like a crosslinked polymer akin to rubber. A rubber ball analogy may go at least as far as the so called oscillating universe model[24]. The analogy suggests that a negative cosmological constant would be dominant when the universe is highly compressed whence gravitation would become repulsive. Not only might this be the source of the energy for a big bang, such repulsive gravity may be important on very small scales so that gravitational attraction does not really increase without bound below the quantum level, that is, as r à0. And, r cannot à0 anyway, by appeal to the uncertainty principle, which is real and not a mathematical artifact or semantic device. So, relativity may not suffer from breakdown at small r.

Still, the Postulate implies that we can nonetheless deduce what is going on at or near the singularity. Thus, GR is rendered “UV complete” because the 2-D (and 4-D) gravitational field is quantum renormalizable[25],[26] and applicable to the highest energy regimes (see below) at the most extreme values of independent and dependent variables. Assuming arbitrarily small distance between two quantum masses, to say that r à 0 is meaningless under Uncertainty, it is simply not allowed. The 2-D G* metric below the event horizon and even far above it is Minkowski asymptotically flat[27] -- a pure spacetime entity in its own right.

Sunyaev Zel’dovich (SZ) effect

Photon frequency is plotted on the vertical (magenta) axis, the ordinate. Distance is plotted on the horizontal (green) axis, the ordinate. Longer wavelength photons would appear nearer the bottom, shorter wavelengths would lie nearer the top. The source of photons would be background stars and/or the CMB.

Figure 4

Sunyaev Zel’dovich effect[28]
 This figure is also derived from Fig. 1. Regardless of the pathway through a galaxy cluster, light is bent by the hyperboloids, even when the ray passes through the thin part of a disk. The hyperbolic (1/r) gravitational fields act like connected parcels of spacetime having a refractive index > 1.  The reverse Compton effect acting on the ray is permanent. The redshift process itself is ongoing.
Integrated Sachs-Wolfe (ISW) effect
Figure 5 depicts the integrated Sachs-Wolfe effect[29],[30]. As above, magenta denotes the photon frequency axis. Green denotes the cosmological distance axis.

Figure 5

Integrated Sachs-Wolfe Effect

A ray of photons cascades down the initial galactic hyperbolic gravitational potential gradient that it encounters, gaining energy with an increase in frequency, going blue. Then it propels up the associated opposite galactic potential gradient, losing energy and going red. But, it does not go as red as it had previously gone blue. Large galactic voids would behave in the opposite manner giving net redshift effects[31].
A photon traveling along the yellow pathway propels down the gravitational field potential gradient, gaining energy – going toward blue. And, when it propels up the next opposite gradient, it loses energy, but not as much as it had gained, producing a net blueshift effect. The expansion of the universe had reduced the height of the gradient in the latter part of the trip so, there was less of a redshift effect that failed to offset the initial blueshift.

Experimentally, the problem becomes discriminating between SZ and ISW effects[32].

Bullet cluster effect

Also, the Bullet cluster effect may be emulated by the presence of supermassive black holes (see Fig. 6) having hyperbolic gravitational fields.

Of course, one must allow for the limitations of this figure. It is merely diagrammatic. It is not meant to represent a detailed true-to-life animation. We realize that there will be strong interactions between the galaxies in the cluster, a few of them even colliding too, with the expected extreme distortions.

There will also be interactions between the central supermassive black holes, which become stripped from their respective galaxies. But, the diagram illustrates how the cluster of SMBHs remains roughly intact, like buckshot passing through a small soft pillow. This intact cluster will be invisible to telescopes yet, it will have an unexpectedly strong gravitational field structure [33]. Such a structure will bend light and appear to us as a disembodied Dark Matter entity by its distortion of the background stars and/or of the CMB (microlensing).

Figure 6

In these colliding clusters, by simple physics, the galaxies are stripped of their central SMBHs (fuzzy grey dots) only because they are supermassive. The blue and red represent the gravitational influence proffered by the galaxies under the 2-D hyperbolic (1/r) SMBH gravitational field postulate (blue) and ordinary galactic inverse square gravity (red). Note the similarity to Figure 7.

 Each galaxy retains its overall structure (except for those that collide), at least initially, because there are potentially millions of large black holes embedded in them. These black holes are not stripped because they are smaller than SMBHs and they are gravitationally trapped in the body of the galaxies like flies on flypaper. Over a long time ever since their formation, these BHs will have come to have their rotations evolve to be correlated, indeed, their rotations become parallel due to the extended frame dragging effect that is active in two dimensions and due to the stronger (1/r) link between them. These BHs will have correlated their rotations with the central SMBH and thus to each other. With so many large parallel spinning BHs embedded within them acting as surrogate central SMBHs, the galaxies retain their nominally flat 2‑D spiral structures unless they undergo head‑on collisions or extremely close encounters. Almost immediately, new central SMBHs will form in each galaxy

The bodies of the galaxies themselves are mutually slowed down greatly by the fact that they contain so much gas, plasma, dust and stars that their whole environments, the entire parcels of spacetime in which they exist, are decelerated. To do this, the masses of the gas and dust must effectively complement the masses of the luminous portions, mainly stars, and these masses must then compete with the masses of the compact central SMBHs. The result is that the dense central SMBHs coast straight through the clouds of stars and gas constituting each galaxy, thus forming new independent structures of their own[34].

Note that the diagram in Fig. 6 is greatly simplified but, it is still suggestive of Figure 6.

Bullet Cluster

Figure 7

NASA, HST image

This diagram suggests that there should be trillions 
   of naked SMBHs floating about in the universe.
 The anomalous velocity dispersion and
galactic temperature gradients, (sections to be added later)

Milgrom’s ao derived

According to the Postulate, the anomalous velocity dispersion of stars in galaxies and galaxies in clusters follows the relation

(1)    avd vo 4 = MGa0    (Milgrom[35]), ao is the MOND acceleration



 M = Mbh            the mass of central galactic SMBH or the..  ……………… of mass in a cluster.  


(2)    voavd  =  vσ   =  (G*Mbh/r*)½  from the paper[36].


(3)    voavd 4  =  (G*Mbh/r*)2  =  MbhGao  

(4)    ao  =  (G*Mbh/r*)2/MbhG  =  Mbh(G* /G½r*)2


(5)    Mbh = ao/(G*/G½r*)2    where r* is the unit vector of orbital radius r

According to the Postulate outlined in the next blogs (#1 & #2, below), this does not mean that Mbh is a constant, but that its value doesn’t matter to ao (being close to an hyperbolic asymptotic value of nonzero orbital acceleration), which will be virtually a constant regardless of Mbh. Only the minimum hyperbolic radius of curvature will vary strongly with Mbh.

And, we do have eq. (6), that is,

(6)     ao/(G*/G½r*)2 = K    where K is based on the incipient or minimum

black hole mass or else on the hyperbolic field asymptote which

should have about the same value for almost all black holes. G*

is estimated in ref. 22.

Perhaps this means that one might say that once a central galactic black hole forms, its additional growing mass does not matter to ao. Or, perhaps this particular initial value of Mbh is the minimum size for a stable central galactic SMBH that can produce a hyperbolic acceleration constant, ao. It must also be true that the SMBH hyperbolic gravitational field has field strength approaching an asymptote (one of the axes) that is independent of black hole mass. All these factors may be in effect.

Mbh in eqs. (1) and (2) are allowed to vary as usual.

So, Milgrom’s ao is now derived in terms of the central hyperbolic (1/r) SMBH galactic gravitational field. One can obtain ao and K independently by theoretical analysis of eqs.  (3), (5) and (6).

Under the Postulate, for ao to be a fundamental constant under MOND, Mbh must be constant from galaxy to galaxy. This is unlikely. The previous analysis recognizes this, especially when it is realized that Mbh affects only the minimum radius of curvature of the gravitational hyperbolic field strength and not the non-zero near asymptotic value of gravitational field strength. These hyperbolic asymptotes are the axes themselves. This nominally virtually constant asymptotic hyperbolic value of ao might be used to estimate the “effective” finite size of the black hole central core. And it might help define the cosmological uncertainty principle.

The hyperbolic gravitational field is also consistent with the galactic temperature gradient as a linear distribution[37]. More about this in a future paper because it is a key indicator.

For the reader,

a problem:

The near asymptotic value of gravitational field strength occurs at around r = 10, say, in arbitrary units, where the gravitational strength hyperbola almost flattens out and its average slope becomes very small. If, at this value of r, the (1/r) hyperbolic gravitational field strength is nearly = 0 (zero is an asymptote) then the HSMBH gravitational field can be said to virtually end, at r >> any galaxy radius. But then, what is the value of this maximum effective r? How big is the DM field, effectively? Use the definition of a right hyperbola as the full hyperbolic field, field strength, FG* = 1/r, and scale it in natural units with the radius of a galaxy = 1 unit. Forget that G*Mbhm and r cannot simultaneously be =1. This is just an exercise.

Dark Matter exists

Dark Matter exists. But, its nature is profoundly different from that which is presumed by the consensus view. Black holes have been said to be crucial in the formation of the universe. They are not only crucial to its formation, but also to its detailed appearance[c].


To be continued


See the related blogs # 1 and #2

Footnotes and Bibliography,

[a]    The basket shaped cavity and the grove around the midsection of the hyperboloid is postulated to support a HSMBH gravitational field that declines as 1/r3 because it represents a spacetime state of the SMBH that is more excited than the state that supports the 1/r field. This implies a quantum-like superposition of states that are detectable simultaneously on cosmological scales.
[b]     The hyperboloid of one sheet is extremely pinched at the middle, down to a radius on the order of a Planck length. The black hole singularity has a putative radius on the order of a Planck length, consistent with the uncertainty principles. To say that the black hole singularity has zero radius is a meaningless statement. It violates Uncertainty. To say that GR breaks down at such singularities is likewise a meaningless statement.  
[c]     The detailed pattern of spiral arms of a galaxy is largely a result of the hyperbolic gravitational field. If gravity declined therein as 1/r2, the arms would wrap around the center like the mainspring of an old alarm clock. Stars would slow down much more rapidly as r declines. Clearly, this is not seen.

[1]     Please excuse the author's unfamiliarity with cosmologists' traditional jargon. Mr. Kentgen obtained a Ph.D. equivalent M.S. degree from the Illinois Institute of Technology in 1985. His nearly complete yet unfinished (due to a funding issue) doctoral dissertation on inorganic physical biochemistry critically involved mathematical modeling. He then became interested in heavy element nucleosynthesis and went on to develop an interest in cosmology and black hole modeling. Since black holes arise largely from galactic and stellar supernovae as do heaviest elements, the evolution of the Postulate presented here seems natural.
[2]      Rubin V., Ford W. K. Jr., Thonnard N. Rotational Properties of 21 Sc Galaxies with a Large Range of Luminosities and Radii from NGC 4605 (R = 4kpc) to UGC 2885 (R = 122kpc), The Astrophysical Journal 238: 471, 1980
[3]      Temperature variations within galaxies  
[4]      Hyperboloid of one sheet
[5]      Large scale structure of the universe (general discussion)   astro-ph/0504097
[6]      Singularities
[7]      event horizon
[8]      R. A. Serway, R. J. Beichner, Physics for Scientists and Engineers, 5th ed., Saunders College Publishing, 2000,,  Kepler’s 3rd law, p432
[9]        Such in-falling material must orbit in concert.
[10]      Brian Greene, The Fabric of the Cosmos, Alfred A. Knopf, 2004, page 254
[11]      The gravitational field is not so limited because it is a spacetime entity. 
[12]      Ignazio Ciufolini,  Erricos Pavlis,   Earth dragging space and time as it rotates    contains an inference about enhanced frame dragging.
[13]      Marcus Chown,  "Gravity may venture where matter fears to tread", New Scientist vol. 2669, 16 March 2009
[14]      Ibid      Gravitational Hyperparabolic (1/r3) spacetime in conjunction with SMBHs is also permitted by general relativity in a spatially n-dimensional parcel of the universe where spatial dimension n = 4 and gravity declines as 1/r(n-1) as implied by GR .
[15]     General relativity allows a gravitational field that declines as 1/r only in 2-D spacetime where gravity declines as 1/r(n-1).
[16]     Birkhoff’s theorem
[17]      No hair theorem
[18]      even Newton’s law of universal gravitation itself
[19]     It is now accepted that no information is lost in the formation of BHs.…. …. …. …. ….
[20]     Black holes have hair
[21]      Kerr metric
[22]     3-D structure of the universe……………………………………………………………
[23]     Sponge, lattice, open cell or cobweb structure of the universe,………………………
[24]     Oscillating universe model 
[25]     L. L. Samojeden, G. M. Kremer, F. P. Devecchi, Accelerated expansion in bosonic and fermionic 2-D cosmologies with quantum effects,,   2-D quantum renormalizable gravitational field
[26]     Jan Ambjørn, Kazuo Ghoroku,     2-D quantum gravity coupled to renormalizable matter fields,  a quantum renormalizable 2‑D gravitational field
[27]      Minkowski asymptotically flat
[28]     Sunyaev Zel’dovich effect,     Inverse Compton effect from hot intragalactic plasma
[29]     Integrated Sachs-Wolfe effect, a redshift effect  
[30]     Integrated Sachs-Wolfe effect
[31]     George Ellis has proposed that the whole visible universe may be adjacent to a huge void of comparable size, not within our light horizon. If so, it would affect all cosmological redshift measurements including those from which accelerating expansion was deduced.
[32]    Discriminating between SZ and ISW effects
[33]    Gary Kentgen, Spinning Supermassive Black Holes, Hadronic Journal (in press), Actual black hole masses may be equivalent to that of whole galaxies.
[35]    Mordehai Milgrom   arXiv:0801.3133v2 [astro-ph] 3 Mar 2008
[36]    See ref. 23
[37]    Galactic hot gas, plasma and dust temperature gradient 

No comments:

Post a Comment