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. Ḡ 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.

 

 

Origin of the Universe

Take a peek at http://cs.astronomy.com/asycs/forums/t/32309.aspx and http://tech.groups.yahoo.com/group/cosmologyandcosmogony/ for a spirited debate on the validity of the HBB theory. The Astronomy forum on cosmogony is a discussion of which I have got really tired recently. I am seeking change-over to an exchange about the implications of a quantum dynamical hypothesis for an inflationary initiation of the HBB.

There seems to be no recognition of such implications. If the universe really did begin as a point particle, called an "inflaton", that appeared in a "false vacuum" by virtue of the tendencey of quantum particles to simply materialize out of nothingness along with their antiparticles, then many questions seem to be settled. But, new ones appear, as is usually the case in science.

For instance, virtual quantum particles that appear out of nothing along with their antiparticles annihillate each other almost instantly. They are called virtual because their lifetime is so brief and they cannot be detected directly. The existence of virtual particles can be proven by studies of muon decay in powerful particle accelerators and by other means. For a virtual particle to remain in existence and become detectable in its own right, it must appear at the event horizon of a black whole, as has been shown by Steven Hawking.

The particle and antiparticle fail to mutually annihilate because one falls into the black hole and the other escapes. If the universe began as such a virtual particle, does this imply that it is or was near the event horizon of an ultramassive black hole?

Our universe may still be in the vicinity of our antiparticle, our anti-universe. It may remain close enough for the gravitational fields of both to overlap. There is much evidence that the reason gravity is difficult to incorporate into unified field theories, grand unified theories or "theories of everything" is that it is unlike the other forces. It can "leak" out of our universe and thus appear to be a very weak force when, in fact, it is the strongest of all the forces. There are quantum phenomena that would allow our universe and our anti-universe to remain near each other for a long time, say, 13.7 billion years, without mutual annihilation.

When quantum particles, which are also quantum wave packets, are detected statistically or even individually, they appear as waveforms and as their interference waveforms as well. In the case of whole universes, these may be regarded as humongous collective quantum states of all the matter and energy that they subsume. Then, there are quantum States A and interference State B for our particle, our universe's waveform, and States A' and B' for our antiparticle or anti-universe. Furthermore, these interference states, in order to be mathematically well described, must be able to hybridize. They can thus form the superpositions of states: A+B, A-B, A'+B', A'-B', A+A', B+B', A-A', B-B', B'+A, B'-A, A'+B, A'-B. Now, gravity can leak between all these states, there being 16 in all. So, the quantity of matter and energy in any one state may be only 1/16 th of the total. This is 0.0625 of the whole. Or else, maybe it is only about 0.04 of the total, depending on how you add up the States and the individual components of the States. If one eliminates the null states, those having a (-) sign, as possessing no gravitational field, one arrives at either 1/22 or 1/10 of the whole that any one state would contribute snd this would represent 0.045 or 0.10 of the whole. If one takes only the primary States into account then only A, B, A' and B' would superpose. Any one of them contributes 1/4 or 0.25 of the whole. There might be other reasonable combinations.

From our perspective within, say, State A, for instance, we can detect the existence of the whole by various means but we can account for as much as, say, 0.25 of it through the inventory of matter and energy in our universe. Maybe we can account for only 0.04 of it. Regardless, we are tempted to postulate some form of Dark Energy and Dark Matter to make the balance sheet work out right. We do this because we are not used to thinking in terms of the quantum dynamical metaphor and because we simply cannot see these other States. They are invisible and intangible.

The mystery of the "missing antimatter" is also accounted for in this scheme. There is no antimatter in our universe because it was all gathered into existence within our anti-universe and its interference wave, the States A' and B' and, perhaps, the other superposed States with primed components.But, there is no Dark Energy or Dark Matter. And, because this "missing mass" is all in some other universe, forever seperated from us by all means except through gravity, we will never be able to detect any of it directly.

Dark Matter is accounted for by MOND, modified Newtonian dynamics. The superposition of States requires that a small constant should be added to the right side of Newton's equation for his Law of Gravity. This small constant represents the "missing matter" in galaxies and galactic clusters. It results from leakage of the gravitational field between the superposed States, which may be so similar that they have galaxies and galactic clusters in almost the same positions but in different orientations. In other words, they are not quite congruent. So, the leakage appears as a smeared out, blurry, spherically distributed small but finite contribution to these cosmological objects' gravitational fields.

The matter and energy inventory of our universe does not balance because we have not taken into account the superposition of States. Statistical analysis of the distribution of energy in the cosmic microwave background (CMB) shows that it is projected upon the sky as if from a flat surface. This implies that the geometry of the universe is flat, not curved like Einstein thought. For it to be flat, however, means that there is an enormous amount of matter and energy in the universe that is unaccounted for. Dark Energy was postulated as a source of this "missing mass", energy having a mass-equivalence through Einstein's famous equation. This idea gained traction when some supernovae were observed at enormous distances. Their brightness showed that they are further away than their red-shifts might indicate if the Hubble constant is applied. This means they are receding faster than is expected. The interpretation has been that this discrepancy amounts to acceleration of our universe's expansion NOW, in the more modern era, even though the more rapidly receding supernovae are observed to have existed THEN, in the most distant past.

It is a backward interpretation that succeeds only because it is perfectly backward and therefore it works - sort of. But, then it runs into reality. To explain this acceleration, Dark Energy was invoked as an ad hoc bandaid to patch the wound that this "observation" made in the s0-called "standard model" of the universe and its origin. So, Dark Energy fills the universe with its "missing mass". But, its nature is unknown and it appears to be an untestable hypothesis. There are conjectures about it - that it may be a new kind of field called "quintessence" that results in cosmological objects repelling each other when they are placed at great distances or that it may result from Einstein's cosmological constant. Ignored is the possibility that the data are being misinterpreted.

Instead, we are all supposed to be happy with an almost supernatural explanation for what amounts to sloppy hypothesizing.

Why do so many distinguished scientists take Dark Energy seriously? It is because they can see no other way past the conundrum that they have themselves created out of whole cloth. They are all trained in quantum mechanics and dynamics but the implication to cosmogony of this, the most well-tested theory in all of science, is so anti-intuitive that they refuse to consider it. So, they go for a hypothesis that is even more anti-intuitive.

Well Stanley, NOW look at the fine mess that you've got us into!

* * * * *

In a future post I shall explain how the assumption that the Hubble constant is indeed a constant has helped get us all into this mess.

You can see which are the leaders of the herd by watching for the ones who are out front when the stampede changes direction. If we look for the leaders at the time when acceleration became popular and when Dark Energy was first proposed, we can tell who might really be responsible for this joke. Then, we might be able to tell better why this mistake has propagated so far for so long. The Science Citation Index might be useful for this. One of its features is a list of citations by scientists and how often that citation was cited by other scientists in their own papers. It is difficult for me to spend much time in libraries. But, I shall find out if the SCI is available online. In another future post, I shall report on my finding.

New Empirical Numeric Model of the Evolution of the Universe

Phenomenological Mathematical Model of the Universe

I think that once galaxies have begun to form, the origin of the universe was quite done and its fate was sealed. Undoubtedly, there will be more progress in the physicodynamics of galaxy formation. Once discrete large scale structures begin to form in the universe, the assumption of the cosmological principle that the universe is homogeneous and isotropic begins to break down. But, before this time, it was probably perfectly appropriate.

I have never seen a mathematical model of the "origin" of the universe and its evolution, growth and development carried through to the present era and beyond. Such a model has been inferred from the data, but I don't think it has been explicitly expressed in analytic mathematical terms. Using Guth's inflationary scenario, specifically his premise of an exponential burst of growth near the very beginning, I have developed a mathematical model that is capable of depicting the evolution of the universe from 10 ^ -60 sec to 30 gigayears and beyond.

By using various choices for parameter values, it is possible with this model to represent a universe that putatively follows a trajectory true to empirical data and transitions to a new era of "neo-inflation" or dominance by dark energy. Or, it can move toward a period of deflation toward collapse in the modern epoch. Or else, it may evolve toward "flat" expansion at a constant rate. Adjustable parameters make it possible for my model to mimic any empirically determined behavior with but very few input values. The plots that I can produce may have significance beyond their graphic utility for visualization.

I use Einstein's natural units to represent the "radius" or radius of curvature of the universe, time and the speed of light. This is the only way that Guth-like equations make any sense and are definable. A plot of these equations, their 1st and 2nd derivatives, H and the expansion of the universe if it had expanded at the speed of light, seems to show a sort of symmetry.

The existence and positions of multiple intersection points where these curves cross in interesting ways portrays an array that might be interpreted as a representation of several kinds of invariance. I am tempted to interpret this array of intersections as a highly symmetric matrix of invariances, also invariant and symmetric in their superimposable, rotational and other transforms of coordinate systems, bespeaking various fundamental constants according to Noether's Theorem.

Revealed here is an interesting problem. I refer to my equations as empirical or phenomenological models that are based fundamentally on theory so that it should be possible to extrapolate successfully into the past and future alike. Using parameters that give a result consistent with the onset of a new epoch of inflation in "recent" times, this form of the model does not provide an early time when the nascent universe could have equilibrated.

Essentially, Guth's idea fixed the major criticisms of the Big Bang Theory by postulating that equilibration occurred during the exponential induction period when the universe was very small and that the transition to exponential growth then locked in the homogeneity that had been achieved. But, with the choice of parametric values giving the required result of that new inflation attributed to dark energy, there is no such induction period.

And, because there are fewer multiple intersection points displayed by this type of plot, it displays less of the above described symmetry than a plot of a type that displays developmental deceleration. Plots showing deceleration show higher "symmetry" and they provide a type of induction period in the traces of their curves. Mathematical physicists prefer theories that possess more of this kind of symmetry.

I want to combine the two types of equations by merely adding them together with variable weighting factors as is done with hybrid solutions to a quantum wave equation. The weights might themselves follow a simple equation that emphasizes the deceleration scenario in the first few moments of the universe's existence and the acceleration scenario later in its evolutionary trajectory. Then, the early induction period would be preserved while the transition to new inflation would be allowed. I want to see if my special symmetry is preserved and see what my being able to do this might imply. I will expand upon this in a future post that will be entitled "The Quantum Universe".

Of course, if the universe really did originate with a singularity, no induction period would be required. Guth's inflation might not be needed after all. If the trajectories of all waves and particles originated at the same point, they would progress throughout the whole with at least some of the same "original" intensive properties, like temperature.

The Big Bang, the origin of the universe, was not an explosion. If space-time expanded from a single point, it is unnecessary to postulate any form of unevenness or turbulence that might give rise to inhomogeneities that would need to be suppressed or quenched. Precisely what cause could be cited that would result in an uneven expansion of space-time or a turbulent beginning with consequent temperature variations? Are not temperature variations simply assumed? Why? The failure of the explosion metaphor must have a consequence.

Gary Kent