Black Hole Singularities and the Possibility of Two Dimensional Gravity

According to general relativity, in a 3-D universe with time, the gravitational field of all compact objects behaves as if the objects are point masses and the field strength must decline as 1/r². In a 3-D universe, therefore it is said, it is impossible to support a hyperbolic 1/r gravitational field. But, black holes are different.

 
Why bother with the whole concept of black holes if they are not different? Collapse of matter into a black hole must not only create a singularity (within the limits imposed by the Heisenberg uncertainty principle) but, the spin rate or orbital frequency of in-falling matter of the black hole must also increase without bound as radius r decreases to values near zero below the event horizon. Attempts to explain away these singularities on the basis of a non-existent quantum gravity scheme are vacuous extrapolations of tentative hypotheses that amount to pure conjecture.

 
Black hole singularities exist. Einstein through Schwarzchild and others say so. Who claims to be more brilliant than these fellows? I appeal to authority here only because it seems to be the only thing that impresses some. If you want to claim that BH singularities are mere artifacts of an inadequate theory, show me the Math.

 
Black holes are different. When matter and energy collapse under an infinitely strong gravitational field to a point mass that is as tiny as may be necessary to explain its properties (not necessarily to zero, the true meaning of infinity), the result is a phase change. Spacetime phase changes are S.O.P. in the repertoire of theoretical cosmologists, like Alan Guth. Let us adhere to the hydrodynamics metaphor used by Einstein in his development of GR. Flat spacetime is a massless superfluid. Helium IV is a superfluid but, it is not massless.

 
To extend the metaphor, it is not hard to imagine that spacetime could undergo a phase change, just as helium IV may. In a black hole this change involves a reduction in dimensionality. This is about the only change available to it. Analysis of the equations of GR shows that gravitational strength, F_g is proportional to 1/r^(n-1) where n = number of spatial dimensions. In a 3-D universe, F_g declines as 1/r². In a 2-D universe, F_g declines as 1/r.

 
So, a black hole must use the gravitational energy of in-falling matter to raise its gravitational potential, the gravitational energy level, to the 2-D “state”. We are starting to talk quantum language now.

 
The shape of this singular BH gravitational field strength diagram, as it is a 2-D entity embedded in a 3-D space, is a nominally flat disk or platter with a potentially infinite radius. Unlike Kerr, I call this topology of the event horizon a “spin disk” because it arises from the infinite rotational and orbital spin rate of matter that has in-fallen toward the singularity. As a spacetime entity, this new phase ignores the event horizon and propagates outward to beyond the edge of the galaxy. It emanates from the central core of the galaxy wherein resides any central supermassive black hole.



Here is one of the non-intuitive consequences of GR. It is known that matter in-falling toward the event horizon must experience time dilation. From our external perspective, we would perceive time for this matter as having slowed and even stopped at the event horizon. Viewed from any point outside the event horizon, time really does stop there. But from its own perspective time does not stop and such matter does indeed drop through the event horizon where it may take part in whatever processes it might (time reversed or not).


There is simultaneously an inverse square gravitational field set up by this time-frozen matter at the event horizon and an inverse gravitational field set up by this same matter that has already in-fallen to the singularity. There is no violation of conservation laws here because no object can feel these separate effects simultaneously. If an object orbits the galactic center in the plane of the galactic disk, it feels the inverse 1/r field. If it orbits on a trajectory not aligned with the galactic plane, if it orbits chaotically, it feels the inverse square 1/r² field.


This has consequences for the analysis of the orbital motion of close-in Milky Way bulge stars like S2 for the determination of the MW’s supermassive black hole mass according to Kepler’s laws. Kepler is valid for the 2-D case as well as for the 3-D case. But, it has to be adjusted for the 1/r gravitational field as does Newton’s law. No deep relativistic calculations are needed. One can determine what changes must be made in Newton’s law and Kepler’s laws by inspection.


Above, I explained how a 2-D gravitational field can exist in our 3-D universe. It must be associated with a black hole having an infinite spin rate as well as infinite density and infinite gravitational field strength. Within the bounds of Heisenberg uncertainty, these singularities must exist. There is no point in trying to explain them away using some kind of unfalsifiable overly advanced unintelligible gravitational quantum sophistry.

 
I show that the hyperbolic 1/r inverse gravitational field can exist as a spin disk surrounding any black hole with said disk extending far beyond the event horizon toward infinite radius. This explains MOND and the anomalous velocity dispersion because hyperbolic 1/r gravity means that orbital velocity, v, around a galactic center containing a black hole, v = (GM_bh)^1/2. That is, v becomes constant dependent only on M_bh and G. This v is not only constant for a given galaxy, it is constant from galaxy to galaxy. This means that GM_bh must itself be a constant, a new fundamental physical constant.


But, G may not be the same G that applies in 3 dimensions. So, I call it G*. Besides by an extension of GR, one might get G* from the M‑sigma relation as well as by the anomalous velocity dispersion. But, the mass of the central galactic supermassive black holes must first be refigured on the basis of the hyperbolic field if very many of the orbits of the bulge stars that were used to get M_bh were coincident with the galactic plane. If all or most of these orbits were chaotic and not aligned with the galactic plane, the BH mass determinations may be okay.


The new fundamental physical constant should actually be written G*M_bh such that G* and M_bh are not independently variable but together form this constant that I call Ḡ. G* is constant only under the influence of the gravitational field of a given black hole.

 
The meaning of the hyperbolic gravitational field of black holes is that MOND (Modified Newtonian Dynamics, suggested by Mordehai Milgrom) is explained without recourse to Dark Matter or to modifications of Newtonian dynamics. Newton and Kepler must be understood in two dimensions, that is all.

 
All of the observations that are said to support Dark Matter as being, say, a huge halo of WIMPs engulfing galaxies and galactic clusters also support the hyperbolic (1/r) gravitational field postulate, even the Bullet Cluster effect.  Dark Matter 3-D maps obtained by analysis of gravitational lensing also follow logically from the Postulate.

The hyperbolic (1/r) supermassive black hole gravitational field is indeed a postulate. This means that there can be no argument against it. It must be taken at face value and carried to its logical extreme whereupon it will be either reduced to absurdity or else found to be correct.

 
When extrapolated to the entire universe, the hyperbolic field mimics Dark Energy too. If Alan Guth’s inflaton particle originated in 2-D space and began to roll down its own hyper-gravitational super-potential slope toward a lower energy 3-D state, the higher energy 2-D potential energy would be progressively transformed in a time dependent quantum-like transition to the new 3-D “ground state”. This potential energy would show up as apparently increasing kinematic momentum of all stars and galaxies in the universe. That is, the universe would appear to be expanding at an accelerating rate.

 
This is an exciting idea because the whole universe is thus to be regarded as a quantum object. It may provide a route to a falsifiable certifiable theory of quantum gravity because 2-D gravity does not lead to a gravitational catastrophe as r tends to 0, and it is renormalizable, a prerequisite for any quantum theory of gravity. This Postulate may point to a means to prove the existence of the multiverse. If Guth is right, Hugh Everett could be right.

 

 

Galactic M-Sigma Relation and the Anomalous Stellar Velocity Dispersion

Galactic M-Sigma Relation and the Anomalous Stellar Velocity Dispersion

Inverse gravitational decline versus inverse square decline


Analyzing the implications of a black hole singularity with near infinitely tight curvature close to the center and what this means to the mathematical form of the gravitational field, one concludes that a postulated singularity requires that black hole gravity declines as 1/r, not as 1/r^2. This effective “infinitely” deep gravitational “point-mass” geometrically implies a hyperbolic gravitational field profile. So, the concept has some bizarre twists.

But, general relativity does not permit a 1/r gravitational field in 3-D + t spacetime. However it does allow a hyperbolic field in 2-D + t spacetime. By GR, gravitational force must decline as 1/r^(n-1), where n = spacial dimensionality. If n = 2, gravity declines as 1/r. So, it is also posited (postulated) that there exists a 2-D, sub-event horizon, hyper-spinning, centripetally induced, infinitely broad disk singularity in all central galactic SBHs. Having mass probably concentrated nearer to the singularity center but being of spacetime in nature, the entirety of the disk singularity is immune to the event horizon of the black hole. It can therefore extend outward to far beyond the galactic rim even to nearby galaxies within a cluster or supercluster.

This 2-D gravitational field is also quantum renormalizable. It is well known that items in a 3-D space can be projected perfectly onto a 2-D surface – the holographic principle. Might this be a simple route toward validatable, falsifiable quantum gravity?

This postulated set of logical statements is immune to criticism. If otherwise logical, it cannot be argued against. It must be experimentally tested. Observation is the only choice to conclusively validate or falsify such an argument. See the definition of “postulate” given below.

Postulate

Definition of a Postulate

• A Postulate is assumed to be a true statement, which does not require to be proved.

More about a Postulate

• Postulates are used to derive other logical statements to solve a
 problem. If a problem is thereby solved, especially if proven by
 other data, the postulate must also be true.

• Postulates are also likened to axioms.

In other words, postulates are to be accepted at face value “for the sake argument” for whatever they may be worth as if they were indisputable axioms. THEN, if a whole argument containing such postulates actually works, there may be much joy. If not, it is back to the drawing board.

Newton’s law of gravity and Kepler’s laws are all easily adjusted to accommodate the hyperbolic 1/r G-field in two dimensions plus time. Kepler’s 3rd law in 2-D is derived from 2-D Newton analogously to the 3-D derivation. It is NOT the same result as if orbiting 3-D objects were limited to an Euclidean plane.

The G-field diagram is hyperbolic when its equal gravitational force contour lines are drawn with spacing in such a way that a 1/r relation is followed to the origin where spacing approaches zero. If the contour lines are then plotted having a z axis, Flamm’s hyperboloid is the result. This is a spacetime diagram, not a gravitational potential diagram.

No inner galactic bulge stellar orbits need be fitted to raw Kepler. Kepler does not define these orbits. Kepler’s laws are used merely to analyze them. The orbits are what they are. Kepler’s 2nd law applies no matter what the form of the central force. The “adjusted” Kepler’s 3rd law follows exactly from Newton’s law of gravity with reduced dimensionality according to GR. It is "adjusted" Kepler that should be used to compute central galactic supermassive black hole mass. See the Gary Kent post on WordPress.com.

There is nothing more to prove. What there is still to be done is to compare with observation.

Mathematically, the constant velocity distribution observed in spiral galaxies is explicitly derived. This means that the M Sigma relation is explained because peripheral stellar v = (GM/r*)^½. Also, Milgrom’s MOND constant, "a[o]", is derived, where a[o] = GM/r*r[∞] = v^2/r*r[∞]. This implies that the universe must have a finite or maximum r because a[o] is an observed finite non-zero quantity. And, M, the black hole mass, may include the masses of many tens of thousands or more of very large stellar mass black holes that are thought to be embedded in every galaxy. The unit vector of r, r*, is used to maintain dimensional integrity.

No modification of Newton’s law is required. But, Newton must be regarded in the context of a 2-D hyperbolically curved spacetime. So, gravity for black holes declines as 1/r and is not an inverse square relation.

All the other effects that have been observed that have been traced to Dark Matter are also explained in this way. These include the anomalous velocity dispersion in spiral galaxies and in clusters, the weak gravitational lensing, the Sunyaev-Zel’dovich, the Sachs-Wolfe and the Bullet Cluster effects.

The hyperbolic G-field parsimoniously explains these phenomena without appeal to any unfalsifiable hypotheses of exotic dark matter. Weakly interacting massive particles and other alien perpetrators of Dark Matter effects have been researched avidly for a very long time. They must be regarded now as unfalsifiable hypotheses because it has become clear that there is no way to prove or disprove their existence or it would have been done by now.

The hyperbolic SBH singular ultra-spin disk G-field might have mass, perhaps like Alan Guth’s inflaton field in the false vacuum. Its mass, but not its hyperbolic gravitational spacetime configuration, could be confined to below the event horizon. The horizon itself could be greatly distorted - including any surrounding plasma or photon sphere. So, a photon passing through the expansive hyper-spin singular spacetime disk would experience therein an enhanced gravitational field, just as if it had passed through a Dark Matter “halo”.

The open cell foam, network or spiderweb structure of the large scale universe is also explained by the extensiveness of the hyperbolic field and its form as a 2-D saddle shape “hyperboloid of one sheet” embedded in 3-D space. Galaxies and galactic clusters will be expected to align so that the hyperbolic surfaces of their 2-D fields tend to coincide. So, even the initial structure of the nascent universe would be influenced by supermassive BHs therein which could have formed very quickly at that time.

They might have been there from t = 0 + an instant, for all we know. After all, if the inflaton particle was like an unstable subatomic particle, it may have decayed into smaller particles including many SBHs. Some have said that the inflaton particle must have decayed all at once. Under these extreme initial conditions, what experimentally validated physical law or fundamental principle is quoted thereby? So, it decays all at once. To what?

In short, the hyperbolic 1/r SBH galactic G-Field explains all the phenomena that have ever been traced to Dark Matter. The hyperbolic G-field IS Dark Matter. Its potential energy profile is generally higher than the profile of an equivalent inverse square G-field. Since m = E/c^2, it accounts for the unseen and unseeable missing mass of Dark Matter. The HBHG field is mathematically derived rigorously and satisfies the mathematical requirements of all observations.

I have written a paper on gravitational decline with distance, but I need a reviewer to help check my mathematics. kentgen1@aol.com

The Hyperbolic Hyper-Massive Black-Hole Universe

The Hyperbolic Hyper-Massive

Black-Hole Universe

Hawking did not buy his own pronouncements regarding the disappearance of information into black holes. Instead, he and some others invented a whole new theory of black-hole thermodynamics. So in a sense, the black-hole event horizon is a real surface. It is sometimes called a "quasi-surface". The center of a black-hole is a physically real singularity. It is constrained only by the Heisenberg Uncertainty Principle. There is no such thing as quantum gravity (QG). How many papers are published in ArXiv on unicorns? By their standards, there should be dozens! So, any appeal to QG to put the Kibosh on black-hole singularities is therefore bogus.

See The Hyperbolic Hyper-Massive Black-Hole Universe and Galactic Gravitational Field (HHBF), which is a paper written for the blog http://garyakent.wordpress.com that describes the e-Model for inflationary expansion of the universe. The hyperbolic hyper-massive black-hole gravitational field is a phenomenological postulate, that is, it is a tentative premise that should be confirmed by experiment or observation and need not wait for theoretical justification. In the case of galaxies and galactic clusters, there is already enough observational support for the galactic hyperbolic super-massive black-hole gravitational field (HSBF).

The point is emphasized that Birkhoff's Theorem and other interpretive principles derived from general relativity cannot apply to any real black-holes. These rules presume that the massive bodies that are considered are always "unperturbed" and are perfectly "spherically symmetric". No real black hole meets these criteria. The rules are good only for approximate calculation, not for"precision cosmology".

Besides, GR should not prohibit a gravitational field that declines as 1/r if a metric is found, similar to the Schwarzschild metric, using assumptions and boundary conditions wherein a singular black-hole is presumed at the outset. If such a gravitational field can be confirmed, the e-Model will serve as more evidence for the existence of our universe as part of a multiverse in meta-time. I appeal for collaborators to help find such a metric.

Hugh Everett may one day be seen as a thinker on a par with A. Einstein. And, John Archibald Wheeler's suggestion concerning the quantum self-interference of probability density waves may be taken more seriously while Everett's declaration of the"reality of probability" as a sort of substance gains credence.

Self-interference can explain the virtual absence of antimatter (AM) in our universe. AM would be confined to our virtual twin, which must exist according to the logical extension of Alan Guth's inflation hypothesis wherein a virtual particle came into existence from a hyper-excited false vacuum which came to exist precisely because of its ultra-high energy level. It would be seen as the deeper mechanism behind apparent "symmetry breaking" and unbalanced annihilation of fundamental sub-nuclear particles and antiparticles to give our universe with matter as the dominant form.

The existence of an interference twin could also be helpful in explaining the hyperbolic field as the resultant of a superposition of states. As the real (to us) expression of a statistical process within the multiverse, we experience only the total sum, the superposed probability density form from which emerges probability, P --> 1. There are ways that such a superposition might affect the shape of a gravitational potential well. Gravity itself may be viewed as a probability vortex or wave in the Einstein Aether. There is much that has not been considered.

If this author was a Mafia gangster

If this author was a Mafia gangster

If the author was a Mafia gangster, a really smooth big-time operator who had to hire a full time personal attorney to defend him from diverse criminal charges, he might admonish his lawyer: “I do not need you to tell me so very simply just exactly what I can and cannot do. I want you to advise me precisely how to do what I want! Capisci?”

Now, the author concedes that GR, as it is most commonly interpreted, regards the hyperbolic black hole gravitational field as impossible. But as a system of sixteen complicated simultaneous nonlinear homogeneous partial differential equations - correct him if he is wrong, his having never actually done this - one must make some assumptions and define some boundary conditions in order just to begin to solve them. When this is done, one determines only the coefficients of these equations, many of which will be zero if one is lucky. The remainder will sum to at least one additional partial differential equation, whereupon more of the terms may cancel and drop out, especially after we apply “suitable” multipliers. This simplifying process is one of the main goals of many of the assumptions and boundary conditions and without which the equations might be unsolvable.

Often, the simplifying assumptions and the artificial boundary conditions may amount to gross oversimplification.

This final differential equation(s) must still be solved (integrated) and so, even more assumptions and boundary conditions must be assigned in order to do so. When this is done shrewdly, the equations can indeed be solved whereupon the results are equations that can be regarded as a set of physical rules that can be tested experimentally or observationally. Like the Friedmann equations under the FLRW metric.

The author finds it difficult to believe that there is no way to select assumptions and define boundary conditions realistically in such a way as to permit the hyperbolic black hole gravitational field. This, especially when, in the case of the Friedmann equations for example, there happens to be a parameter designated ρ/ρ_crit which determines whether the whole universe is spherical (closed), flat (perfectly Euclidian in both time and space) or hyperbolic (open).

The author knows that this is not quite relevant, so please do not focus on this stupid little example and try to tear it to pieces. But, this is mentioned just to show that one can redirect solutions of GR toward hyperbolic results so very easily just by means of solutions having some mere adjustable parameters.

Einstein cannot have been so inflexible that he would have written a theory that could be so rigidly used to prohibit reality. Such a prohibition would be a XXX atrocity wrought by a Grade AAA genius! Ha Ha!

Let us not promulgate or propagate any such atrocities of our own.

Author’s challenge: a case of fine Spanish wine (NOT Italian; capisci?) to the understanding personality who can help him find a way to “force” GR to do want he wants! I am a biased scientist. But, at least I admit it.

In the meantime, all he is saying below is that there is sufficient reason to go ahead and allow the hyperbolic field as a postulate. The ideas below are not meant to be picked apart and eaten alive. But, they should still be digested. They are not logically necessary and sufficient, so demolishing them may be pointless. They are meant only to illustrate the notion that to allow the hyperbolic field as a postulate might make good practical sense.

As acknowledged above, the hyperbolic black hole gravitational field (HBHF) is said to be prohibited by common very reasonable interpretations of general relativity. But, the consequences of finding some realistic loophole, some valid formulation of the HBHF are potentially momentous. They may even be capable of causing a revolutionary paradigm shift in the science of cosmology. Reasons that could motivate the search for some means to validate the HBHF are manifold.

1.) The HBHF field can explain the anomalous orbital velocity distribution of stars in galaxies.

2.) The HBHF can explain anomalous velocity distributions of galaxies in galactic clusters.

3.) HBHFs can explain the dependencies and magnitudes of the Sunyaev-Zeldovich effect. It can even explain the progressive changes in the SZ differential redshift offset effects that are seen when this phenomenon is observed to occur through large voids closer and closer to Earth.

4.) The HBHF can explain the apparent offsets in the barycenters of colliding galactic clusters – the so-called “Bullet Cluster effect”.

5.) The peculiar galactic thermal distribution effects can be traced to the HBHF.

6.) The HBHF can more fully explain gravitational lensing phenomena.

7.) The HBHF can explain the inhomogeneity that is seen to have developed in the early universe, said inhomogeneity having been present since before the time of “recombination” of electrons with atomic nuclei. (This inhomogeneity probably persisted as the hot plasma produced from the Big Bang “recombined” to produce now greatly redshifted emission of the cosmic microwave background radiation (CMB). Acoustic variation and long prior quantum perturbations are said to have been insufficient to fully account for the deviations that are now observed in the CMB.)

8.) The HBHF process in 7.) can provide a confirmatory rationale for the Inflation theory of cosmogenesis. An Inflationary Big Bang, with the “inflaton” behaving like a hyper-massive, decaying, excited, quantum, fundamental point particle might have resulted in a large number of big primordial black holes as well as a lot of electromagnetic energy and many subatomic particles. This decay debris as these primordial black holes, with their super-extensive hyperbolic gravitational fields, would serve to induce an unusually broad gravitational “halo” effect similar to the one postulated for Dark Matter that is supposed to have been largely responsible for the inhomogeneity observed today in the CMB and in the actual observed distribution of galaxies.

9.) An extension of the HBHF hypothesis to the whole universe can provide a mechanism for a positive lambda in the LCDM Friedmann model of the universe. But, the label “lambda cold dark matter” might be replaced by the “lambda apparent cold dark matter” or LACDM model, since “cold dark matter” will then have been seen to be utterly superfluous.

One angle to deal with criticism along the lines of Birkhoff’s Theorem and its siblings might be to postulate that a black hole is wholly a quantum object so that its gravitational field is really a quantum field of a different form from the kind of gravity in GR. Perhaps Alan Guth’s “inflaton field” is related to gravity, but being hyper-excited is not actually gravity, exactly. And, it could have a hyperbolic normalizable form because it originates, not in a Hugh Everett style meta-universe, but in an “infra-universe” or “sub-space” of fewer dimensions.

So, even according to present interpretations of GR, it could then indeed be hyperbolic in its mathematical description. This “Many Worlds” interpretation of the nature of black holes and/or the Inflaton Particle may include laws of physics that no longer pertain except in regard to black holes, especially since black holes involve physically real singularities. Inside black holes, the laws of physics not only may break down (so it is impossible to say what rules may be valid and what rules are struck down), but may be delocalized outside the singularity and even far outside the event horizon. And, yes, the author knows that he speaks of black holes and the whole universe in the same breath.

After all, if the universe was once a quantum entity, then it still is. Macroscopic quantum effects should still be discernable in larger systems than in just tiny globs of Bose-Einstein condensates. Would super-massive black holes be large enough for you? Yuk Yuk!

The contention that some future theory of quantum gravity will erase the physically real singularities in black holes is like a dream. The author thinks that theoretical physicists have been thrashing around for long enough. It is time to acknowledge that no such TOE or GUT will be forthcoming. No GUT has been proposed that uniquely and competently predicts anything new that has actually been verified, is falsifiable and actually unifies what it claims to unify.

So yes, a theory of quantum gravity has an anticipated feature wherein it will not result in any singularities or event horizons. And thus, it will have no black holes. But, there is a catch:

Recently, attention has been drawn to the fuzzball model in string theory. Based on calculations for particular situations, the hypothesis suggests that, in general, the individual states of a black hole solution might not have an event horizon or singularity. But, for an actual observer, the statistical average of such states may appear just like an ordinary black hole in the lenses of general relativity.

(to be continued)

If this author was a Mafia gangster (continued)

If this author was a Mafia gangster (continued)

In other words: What’s the difference? No observer can experience an individual quantum state, but only the sum of said states as a total probability density of states that emerges ultimately as P = 1. So, the quantum quasi-singularity of a black hole must appear as if it is a real singularity. This could be construed as quantum relativistic existentialism. Seeming is being. Or, according to logical positivism, if it walks like a duck, quacks like a duck, flies like a duck and looks like a duck – it’s a duck. And, if it is roasted, it will smell and taste like duck too.

People like to forget the correspondence principle. If general relativity is real, quantum relativity must endorse it and vice versa. In a GUT or TOE, one can never be used to negate the other or else they are both false.

Once again, all that the author is saying

herein is that there is sufficient reason to go right ahead and allow the hyperbolic G field as a postulate. We shall figure out the theoretical justification later. The ideas below are not to be gnawed apart and eaten alive. But, they should still be digested. They are not at all logically necessary and sufficient, so their demolition may be pointless. They are meant merely to illustrate the notion that to allow the hyperbolic field as a simple plain postulate might conceivably make good practical sense.

A 2-D origin of the universe is not inconceivable. And, 2-D components of a non-spherical 3-D gravitational field are not ruled out. One can imagine that 2-D cosmogenesis or galactic orbital motion around a black hole was conceived when such motion or even the entire universe began to unfold or deconvolve from a compactified form, perhaps like opening (or closing) a child’s “pop-up” book. So, the universe may be deconvolving and galactic SMBHs are reconvolving – they are unfolding and refolding exactly as they should*.

The aforementioned rationale would include Guth’s hypothesis of an ultra- energetic hyper-massive “inflaton” point particle in a super-excited “inflaton field” that decomposed, decayed or deconvolved from the a false vacuum, thus forming our universe. It seems unlikely that the inflaton particle would have decayed directly into gazillions** of photons and little fundamental particles directly, all at once. This is not the way short lived excited particles typically decay. It probably split first into several quantum “fields” (but NOT gravity because gravity might have been already present, perhaps as the ground state of the inflaton field at the floor of the false vacuum) then thousands, and then millions of large black holes (the enhanced gravitational fields of which constituted Dark Matter) and simultaneously and/or subsequently into a lot of electromagnetic energy as well as many small particles.

The inflaton gravity-like field itself also surely would not have collapsed or changed all at once. Its time dependent quantum transition might have been a process that may still be going on. If the universe was once a quantum entity, then it still is. Then, the present epoch’s continued breakdown of the residual inflaton field may act like gravity in whatever proper kind of spacetime it may need to give a hyperbolic asymptotic effect for the whole universe (so that it would have a higher potential energy than the ground state inverse square field).

In an infinite array of 2-D slices (if necessary to allow the HBHF) the universe HBHF’s ongoing stacked or packed 2-D asymptotic cross sections might devolve or transform into the lower energy 3-D inverse square gravitational field. This process might then result in acceleration of the expansion of the universe and putative Dark Energy.

Or else, a black hole is a tunnel or portal to another universe (Everett’s “Many Worlds” interpretation of QM) with different physical laws spilling over into our world and which simply do not prohibit the HBHF.

Another avenue might be to say that a super-massive black hole galactic gravitational field can be hyperbolic by virtue of analytic pure geometry in a non-Euclidian space, by an appeal to Schwartzschild’s analysis which certainly includes a potentially non-Euclidian metric and to Kretschmann’s invariance which does not depend on any coordinate system. Then, if proper assumptions are made and correct boundary conditions are set, GR cannot be seen to override these sets of principles, however fundamental GR itself may be.

As well, under the circumstances that would allow F = GMm/kr, GR might not be seen to trump the symmetry argument that is used to extend the asymptotic hyperbolic field to the far right on the ordinate of a gravitational field strength diagram. (Such a diagram needs to be given some latitude because it is a plot in 2-D Euclidian space, LOL). Symmetry representation is one of the most powerful tools available to the quantum physicist.

With additional assumptions or slightly different boundary conditions, the Schwartzschild treatment and Kretschmann’s invariance will still work if the overall geometry of spacetime in the broader galactic zone around a black hole is not Euclidian, such that this whole local space could be strongly hyperbolic. And, there may be a way around the necessity to consider gravity as always operating under an inverse square relation, especially if there are “perturbations” that are really more like very strong distortions (like a train wreck distorts the rail cars) so much so that perturbation principles cannot reliably be used for a mathematical description of any real black hole.

The spacetime geometry in the distortion zone of a galaxy or galactic cluster containing black holes may be so strongly warped and hyperbolic in nature that any type of field, hyperbolic or not, can exist, persist and never cease to desist. Yet the overall hyperbolic or “open” geometry of the universe may be counterbalanced by the mere existence of all the matter and energy that it contains so as to “behave” like it might be flat. But acceleration of Hubble expansion means that, if the universe is not open at present, it “soon” will be.

By the way, the hyperbolic gravitational field, being quantum normalizable, could be characterized, perhaps, as also pertaining to the Higgs field and the Higgs boson.

Therefore, the author thinks that there is something fishy about the way GR is used and Birkhoff’s Theorem and its siblings are cited in order to put the kibosh on the HBHF.

All this author is saying, once again, is that there is sufficient reason to go ahead and allow the HBHF as a postulate. The above notions are not meant to be picked apart by intellectual sharks, however kindly, gentle, articulate, well meaning, gifted and dedicated. These ideas are not logically necessary and sufficient, so their utter demolition may be pointless anyway. They are meant only to illustrate an idea, not to prove it. This is that to allow the HBHF as a postulate might make very good practical sense, eventually.

Let us do this in the same way that Louis DeBroglie promulgated the postulate that the Bohr planetary model of the atom that he defended simply did not and could not undergo an “ultraviolet catastrophe” as classical physicists insisted that it must. DeBroglie almost single handedly invented quantum mechanics by means of his postulate. But, he had a little help from Albert Einstein, Irwin Schrödinger, Werner Heisenberg, P.A.M. Dirac and a few others.

This is what is needed now. Some help. If you or someone you know can collaborate on a paper for the Astrophysical Journal or some other platform, please consider it.

Furthermore, allowing the HBHF may provide yet another link between quantum mechanics and general relativity. There are a number of links already and when we forge enough critical connections we will have a ready-made unified theory of quantum gravity without having made any special fuss. We need not invent seemingly unfalsifiable, incompetently unpredictive, almost infinitely numerous, unmitigated psychedelically novel and inordinately complex hypotheses. The author hopes that he is wrong but, such as these look like a whole boatload of Aristotelian theories of baroque “epicycles” that might accomplish little new that is uniquely proven. That is, except to satisfy the anal retentive urges of some who may otherwise be very fine workers, what purpose is to be served?

Theoretical physicists have long been fascinated by Eastern philosophies. They say that many principles of modern physics, including relativity, are reflected by philosophical concepts therein that are millennia old. The philosophical point that they choose to ignore is the tenet of “Yin & Yang”. Why should we not be satisfied with “two sides to the same coin”? Quantum mechanics and general relativity are not truly in opposition in any way. They do not address the same issues. They may be mathematically incompatible largely because they were assembled by different people who used different symbolic conventions and starkly different initial concepts. But, why should one necessarily be able to express gravity on an exceedingly small quantum scale? What for? Why should we be able to compute the properties of a galactic cluster from quantum principles? Why?

* After Desiderata by Max Ermann

** A gazillion is a number about equal to the total number of massive bodies, tiny fundamental particles and photons that were ever present as the inflationary Big Bang proceeded toward the time of “recombination” and far beyond. It is much larger than a googolplex. LOL

. . . Mafia Gangster (continued)

. . . . . . . . Mafia Gangster (continued again)

So what? If computations show that gravity becomes infinitely strong when the distances between even very tiny almost massless objects becomes excruciatingly small, maybe we can learn something about what may have held the “inflaton” infinitely dense point particle together before the Big Bang.

Gravitational Field Strength

and

Potential Energy Diagrams

for the

Inverse Square and Hyperbolic Cases

Figure 1

Figure 2

The Figure 1 caption remarks that interpretations of Birkhoff’s Theorem and its siblings may well be misinformed. One such common misinterpretation is outlined in detail by Kristin Schleich & Donald M. Witt, A simple proof of Birkhoff's theorem for cosmological constant, arXiv:0908.4110v2, wherein they prove that the common belief that Birkhoff's Theorem implies staticity is false for the case of a positive cosmological constant. So, it is not the various theorems themselves that may be a problem, it is the ways in which they and GR are commonly interpreted which could be at fault.

Let us use whatever type of realistic interpretation of GR equations that might be needed to allow the HBHF.

Figure 2 presents plots of the equations

1.) y = ln(x)

and

2.) y = -1/x +1

according to common axes and equally scaled in such a way as to accurately represent the overall relative shapes of an inverse square gravitational potential energy diagram (2.) and a hyperbolic gravitational force P.E. diagram (1.). Note that P.E. keeps increasing without bound to the right in the case of the hyperbolic black hole P.E. trace which is actually a plot of ln(x) here.

What this really might mean is that the cosmological influence of black holes might extend to infinity as a strong influence, or to whatever passes for infinity in our universe. So, the black hole gravitational effect may pervade the space well beyond a galaxy wherein it is contained, far beyond the space in a galactic cluster wherein BHs may be found and beyond even the envelope of galactic super-clusters or “walls” into large voids where the HBHF’s slow “dilution” going deeper into the void could amplify the effect of such a void vis a vis the Sunyaev-Zeldovich effect.

In other words, the hyperbolic super-massive black hole gravitational effect might mimic a “halo” of Dark Matter that envelopes galaxies and galactic clusters. It could even deepen the difference between the gravitational fields present in large superclusters or galactic “walls” and the relative absence or “dilution” of said fields by Hubble expansion effects deep inside voids.

Growth of SMBHs over long periods of time by accretion in the nuclei of galaxies might cause their super-extensive hyperbolic gravitational fields to further deepen the differences between walls or super-clusters and large voids so that a process or time-series of change in the SZ effect is observed as said voids are examined closer and closer to earth. This may impact the evidence interpreted in support of acceleration and “Dark Energy”.

If the hyperbolic black hole galactic gravitational field can be generalized to the entire universe, its false vacuum transformation or time dependent quantum-like transition to a ground state inverse square gravitational field may have begun with the Big Bang. And, it might be characterized as a process that is still ongoing. So, false vacuum potential energy from a higher energy hyperbolic gravitational form, as in the red curve, might become available kinematically to objects under the influence of the familiar inverse square gravitational potential energy, consistent with the black curve.

Perhaps the nature of black holes includes re-establishment of an infinite series of false vacuum 2-D slices and a stack of excited inflaton fields inside the event horizon that can penetrate the horizon and act like the hyperbolic field that the author postulates.

In Fig. 2, acceleration of Hubble expansion would become apparent after the curves begin to substantially diverge (diagrammatically and not to scale) at “about” x » 1.5. The present time, t, or the present scale factor of the universe, a(t) could be represented to be “located” at maybe around x (or y) » 3.5 so that acceleration becomes apparent at maybe around 30 - 40% of the way toward t = 1, the present, or toward a(1) = 1, the present era scale factor.

If we took the time, we could make these diagrams to scale so that actual predictions or depictions of real observations could be symbolized. Crudely diagrammatic or not, this scenario seems to be close to what may have been actually observed. Of course, it may be said that these curves were shrewdly constructed in an artificial manner that was deliberately meant to show this very thing. But, it was too easy to be an accident and this author is not smart enough to have contrived it.

Look at the enormous difference between the red curve and the black curve to the left of r = x = 1. This difference grows and becomes virtually infinite as one moves his attention further to the left, approaching the abscissa. Maybe this would provide a rational for the spark of initial inflation, which may then be said to have ended at r = x = 1, not after just a few seconds. Then, to the right of r = x = 1, the curves diverge again as the universe experiences acceleration or “reinflation”, gaining new vigor from the infusion of energy from the hyperbolic field’s current residual false vacuum gravity-like field.

Well intentioned, sincere, dedicated and very intelligent people

have tried to prove that the hyperbolic black hole gravitational field is impossible. They may sometimes use direct application of GR without prior recourse to any metric. Sometimes they have used simple geometry and the definition of luminous, gravitational or magnetic flux. Such geometric arguments are circular because these definitions presume what is to be proven (they beg the question).

But, one has to solve GR for a metric first, and then use even more assumptions and boundary conditions to solve for a useful equation(s) that can be experimentally or observationally tested. Of course, using definitions that presuppose their conclusion or using the conventional multiple layers of assumptions and boundary conditions, one must logically arrive at the notion that the form of the gravitational field has to be an inverse square relation in any universe with 3 spatial dimensions. Many Worlds notions do not appear in GR.

It seems as if there is actually no way to explicitly acknowledge the physical reality of a black hole singularity in any way in superficial treatments of GR. Unless such proofs explicitly treat the singularity as physically real, and which is not merely another simple internal “distribution of matter”, they may end up proving nothing. Whatever odd geometry, queer boundary conditions or kooky assumptions may be realistically necessary to admit the HBHF, they should be considered.

Let’s face it. Black holes are real and unique. We need to treat them mathematically this way, as if the central singularity is not a myth, nonexistent TOEs or GUTs notwithstanding. Some observably exceptional properties must propagate far beyond the black holes’ unobservable event horizons or else black holes are just ordinary objects in an increasingly dull universe.

So, if this is to become the day of the ghostly GUT (somewhat like The Day of the Triffids or, perhaps, The Invasion of the Body Snatchers , or even The Night of the Living Dead – heh heh!), cosmology may already be “virtually” dead. We may not have to wait another 27 billion years for the universe to expand beyond cosmological causal contact.

Finally, speaking of renormalizability, the hyperbolic black hole gravitational field may be renormalizable precisely because it is not represented by an inverse square relation. So, perhaps this would be a means to force gravity into the rigid klogs of quantum dynamics. The advantages and therefore the motivation to admit the hyperbolic gravitational field, even as it may be an unlikely postulate, may be much greater than anyone thinks.

Figure 3

In Fig. 3, correction: reference should have been made to the "excited state of the false vacuum 'inflaton field' ". Sorry.

It may seem like we must postulate a prior existence of the inflaton particle's excited inflaton field as an hyper-excited gravitational field that existed when the inflaton particle came into existence as a very high probability "virtual" particle that has yet to find its annihilation partner. Maybe this is the real meaning of the "Ekpyrotic Theory" of colloding "branes".

Figure 4

We could keep Newton for laughs by joking that F = GMm/r^1.999 , there being no such thing as a truly real and distinct perfect sphere in the locally distorted geometry of our universe, at least not anywhere near black holes. What does in fact happen to a gravitational field if it is not spherically symmetric as all the theorems presume? If it can be used at all, might perturbation theory have to introduce an hyperbolic field component? This is almost Newtonian F equation may be renormalizable too because it is not quite an inverse square relation. Ugh! This could be a form of MOND, modified Newtonian dynamics. Everyone knows that all modified gravitational field theories are intrinsically illegitimate (LOL).

Click to see this image series in detail:

http://www.fotothing.com/Gak/photo/d98a611bae38b8ed1ac943e8344717d1/

Dark Matter is an unnecessary ad hoc fix

Dark Matter is an unnecessary ad hoc fix to fill in the blanks in the Friedmann model under the FLRW metric. Galactic supermassive black-holes exist as true physical singularities according to the Kretschmann invariant and Schwartzchild's analysis. Therefore, as point masses, they must possess a hyperbolic (1/kr) gravitational field, NOT a field that falls off as 1/r². Now, k = constant = 1m, S.I., for dimensional integrity. It is not true that GR cannot tolerate hyperbolic spacetime geometries. "The universe is hyperbolic." said Albert Einstein in his classic paper of 1915.

An hyperbolic field will give constant orbital acceleration to orbiting bodies as far from the center of a black-hole as we might like to measure. This means that bodies near the periphery of a galaxy should seem to move at constant velocity because rotational acceleration does not drop to near zero there as with a 1/r² inverse square law. This constant velocity distribution effect has actually been measured and has given rise to the notion of Dark Matter.

Gravitation does not fall nearest to zero between galaxies in a cluster either. So they too can bend light and affect redshifts in ways that mimic Dark Matter. The rotation of galaxies in clusters is also influenced by the black-holes that they contain with their 1/kr gravitational potential profiles. The not quite counterbalanced redshift effects in the Sunyaev-Zeldovich phenomenon are influence by the hyperbolic galactic and galactic cluster gravitational fields that exist as light falls out of such clusters and super-clusters into a large void and as it climbs out of it again after the universe has expanded by another billion light years or more.

Scientists are mapping, not Dark Matter, but the huge extent of the network of hyperbolic galactic and super-galactic gravitational fields that behave like Dark Matter because of the mathematical properties of the hyperbolic gravitational field are similar to That expected for Dark Matter.

Primordial massive and supermassive black-holes with their 1/kr galactic gravitational fields can also mimic the “halos” of dark Matter that are postulated to have existed just after the big bang and before the emission of the cosmic microwave background. There is nothing that Dark Matter explains that cannot be accounted for just as well or better by the hyperbolic black hole gravitational field.

The hyperbolic 1/kr supermassive black-hole galactic gravitational field explains “the Dark Matter Effect” without Dark Matter and it is more parsimonious and is a falsifiable hypothesis, unlike Dark Matter

The conditions for validity of Birkhoff’s Theorem are not met for real black-holes. Therefore, Birkhoff’s Theorem does not apply. It sometimes may be used as a first approximation, but it cannot be depended upon as a rigid rule for precise calculations. “The physics near the extreme curvature of a black-hole singularity is not well defined”. This covers Birkhoff’s too.

By the way, any entity that possesses mass by virtue of its motion will be influenced by the gravitational fields that it encounters. It is not so much that a gas mimicking Dark Matter may be very much colder than other gases that such an entity might encounter, but whether such a gas may be much denser. But absolute zero is absolute. Only ground state vibration modes are allowed for gases at absolute zero, translational motion does not exist at K = 0 because it implies a temperature, T > 0 K. So, gases must not exist either. They must be solid crystals. Also, such ground state vibrational modes are only for multi-atom molecules. Intergalactic gas is almost non-existent, is not denser and is not a factor, so it cannot mimic Dark Matter.