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
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
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).
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