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/ρcrit 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)
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
Gravitational Field Strength
Potential Energy Diagrams
Inverse Square and Hyperbolic Cases
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.
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.
We could keep Newton for laughs by joking that F = GMm/r1.999 , 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).
The Neo-Cosmology Blog As skeptical astrophysicists, cosmologists or scientifically interested persons valuing hard, tangible proof of purportedly revolutionary theorems, theories, hypotheses or paradigms of cosmology or cosmogenesis, we welcome the new (neo) cosmology that is forming before our very eyes. But, we need and often proffer hard evidence with no unstated assumptions or hidden postulates. This is not a blog for mere chat. This is a blog for significant contributions.