Galactic M-Sigma Relation and the Anomalous Stellar Velocity Dispersion

[Gary Anthony]

Hypothesis: Supermassive black holes must develop incredibly high spin rates, as would be measured by an observer under the event horizon. They condense initially out of massive supernovae and then from stellar components that orbit in concert within the innermost stratum of the central bulge of spiral galaxies. Due to this ultra high spin rate, nearing infinite rate below the event horizon, matter in such black holes never has a chance to compactify to a singular point with virtually infinite density. Instead, it flattens not to a mere point mass or to a simple ring singularity, but to subtend a "planar" subset of spacetime that is only 2 dimensional. It becomes a huge flat spacetime disk. But, this spacetime parcel still has mass.

Oddly enough, this explains the strange correlation of the velocity distribution of stars in spiral galaxies wherein rotational v of outer stars correlates with the mass of the central supermassive black hole, the M-sigma relation. There should be no such correlation if gravitational force for black holes is an inverse square central force. This notion shows that no exotic dark matter is needed to explain this phenomenon. But, Dark Matter is still implied by this hypothesis.

Because by extreme contraction under rapid spin of matter to “almost” a point singularity with “almost” infinite density (“almost” means “to below a Planck distance”), the gravitational force therein is so intense that it is asymptotic in behavior: it is hyperbolic (1/r) in nature and it changes the nature of spacetime. So, it emanates from an extensive centripetally induced 2-D “disk” singularity. A peculiar result is that for stars nearer the galactic periphery, stellar velocity v' = (GM/r*)½ , that is, it is a constant that is totally independent of r. (r* = the unit vector of r, for dimensional integrity.)

Therefore, as is actually observed (the M-Sigma relation and the anomalous velocity distribution in galaxies and clusters) that this hyperbolic 1/r gravitational field of the supermassive black hole disk singularity can reach to the galactic periphery and far far beyond. And, because it is so much more extensive than an inverse square force, it has an effect on other nearby galaxies which also may have supermassive black holes with similar gravitational forces in play. This possibility explains all the phenomena associated with Dark Matter. It does not deny Dark Matter. It clarifies it.

This massive flat relativistically plausible spacetime ultra-spin disk is a hyperboloid of one sheet. It has a saddle shape, its being embedded in a 3-D + time universe. The curvature of the hyperboloid does not become apparent until r becomes very large, far beyond a galaxy. So, to engage other galaxies with their own SBH hyperbolic fields, the "plane" or surface of this curved sheet will align with them more readily because it is not really planar or “flat”.

This alignment is a way to account for the observed large scale network or spiderweb distribution of galaxies within clusters and superclusters. It also helps account for the primordial structure of the universe, as supermassive black holes may have been very common in the beginning.

Newton’s law will accommodate a 1/r gravitational field only if spacetime is limited to 2 dimensions plus time, by general relativity. Kepler’s laws can be modified to accommodate a 1/r field because these laws assume Newton, and Newton’s law needs only to be rewritten for gravitational 1/r 2-D spacetime.

This 2-D spacetime parcel possesses mass, like the highly excited inflaton field postulated by Alan Guth. Also, since it is spacetime in nature, it is immune to the event horizon of a black hole. Therefore, it can extend as far outward as is necessary to account for its effects - the real meaning of infinity.

I have written a paper along these lines. But, I need a reviewer to help check my mathematics.

kentgen1@aol.com

[Gary Anthony]

The potential energy profile of the hyperbolic 1/r supermassive black hole galactic gravitational field is generally higher than the profile of the equivalent inverse square profile. So, the difference between the P.E. of the hyperbolic field and the P.E. of the inverse square field is a real energy difference. Because M = E/c^2, this difference represents mass – matter that is unseen and unseeable. That is, this is Dark Energy.

[Gary Anthony]

OOPS! It is Dark Matter.

Sorry.

[Hugechris]

This very interesting, would be keen to look at the paper, do you produce new solutions for spinning black holes?

[acey]

When you posted your theory here a few months ago I pointed out that general relativity in 2 space dimensions is trivial, therefore what you were trying to do was mathematically impossible.

http://stargazerslounge.com/topic/135822-black-holes/page__hl__gravity

[Hugechris]

To map the whole field to 2D is not practical as a solution. However the gravitational field perpendicular to the disk has a component that varies as 1/h where h is the perpendicular distance from the galactic centre, this would have an impact over distance of order the size of the galaxy. To come up with a "dust solution" outside a rotating black-hole without resorting to dimension reduction would be interesting.

[Gary Anthony]

Newton's law and Kepler's law in 2-D spacetime is not trivial. It works because general relativity allows gravitation to exist in 2-D so long as it follows an inverse relation rather than an inverse square relation. The Kerr metric does not go far enough. It does not treat the consequence of a real singularity under the event horizon wherein angular momentum of in-falling matter must continue to increase toward infinity. Reality does not end at the event horizon. Of course, I agree that infinite density and infinities of any kind are not too likely in the case of black holes because they should still be covered by the Heisenberg uncertainty principle. Spacetime cannot contract to less than a Planck distance or a "Planck radius". But, when it does so contract to form a BH singularity, its huge density and spin rate will cause extreme distortion of the tiny spacetime parcel represented by the spacetime volume nearest the singularity. I postulate that this parcel will distort to a 2-D flat spacetime disk singularity, not a mere ring singularity. Because it is spacetime in nature, it can ignore the event horizon and extend far beyond even the galaxy itself. Being a BH singularity under the Heisenberg limits, it still has mass, though the mass might be constrained to exist beneath the event horizon, which would also be similarly distorted. The ergosphere and frame dragging near the surface of the singular disk may be important (allowing the 2-D surface to appear to have thickness). But, what really matters is the hyperbolic 1/r decline in gravitational force with distance. This explains the M-sigma relation and the anomalous velocity dispersion observed for spiral galaxies because one finds that stellar v = (GMbh)^1/2 which is constant depending only on Mbh. It is derived directly from F = GMm/rr* where r* is the unit vector of r for dimensional integrity. The various forms for orbital velocity and acceleration are derived exactly like the corresponding "raw" Newtonian quantities. But, Mbh may have to include the masses of tens of thousands of massive stellar black holes that are embedded in a galaxy. Still, a more parsimonious result will be hard to find.

Newton and Kepler are not used to "model" the orbits of inner bulge stars. They are used to analyze them. This is a big distinction. But, a model based on the hyperbolic gravitational field would look just like a model that uses "raw" Kepler and Newton. But, Mbh would have to be treated like a fit parameter. In this case, Mbh would be seen to be much smaller than the corresponding value for Mbh that would be used in a successful raw Kepler/Newton model. I call such a hyperbolic field model an "adjusted" Kepler/Newton model. Mind you, this is not "modified Newtonian dynamics", although MOND follows directly. That is, MOND can be derived by using the forms from the hyperbolic BH gravitational field. I think Mordehai Milgrom would be interested, especially because his hypothesis can be derived without ruining general relativity. I fault Milgrom only for ignoring the implications of supermassive central galactic black holes.

Dark Matter as WIMPs or other exotic matter will never be found. They have been searching for decades now and if they have not found it by now, they never will. But, Dark Matter exists. It exists in the difference between the hyperbolic gravitational potential energy profile and the equivalent inverse square or "parabolic" P.E. profile. The hyperbolic profile is generally larger. So, delta(Mbh) = delta(E)/c² . Delta means the difference between a raw Newton P.E. profile and an adjusted Newton P.E. profile. One could argue whether this delta is real. But, the concept can be extended to the whole universe and the "inflaton" excited false vacuum field. The idea is that transition from the initial false vacuum field to the "ground state" gravitational field in the present universe would be a transition from a 2-D universe to a 3-D universe (plus time), Such a transition presumes a quantum-like superposition of states and it would be time dependent. There is a point where the false vacuum field and the ground state field cross over whereupon the false vacuum P.E becomes realized as actual "expansion of 3-D space" and apparent kinematic repulsion between galaxies, clusters and superclusters. In other words, the hyperbolic field concept can be extended to explain Dark Energy.

One cannot hope for a more parsimonious treatment of DE and DM that still subtends Alan Guth's inflationary universe, general relativity, Newton, Kepler and quantum dynamics.

[Gary Anthony]

When you posted your theory here a few months ago I pointed out that general relativity in 2 space dimensions is trivial, therefore what you were trying to do was mathematically impossible.

http://stargazerslou...ge__hl__gravity

It is not trivial and I supply QED. Impossible is in the eye of the beholder, like the splinter in one's brother's eye that becomes a log in one's own.

[Gary Anthony]

By superimposing a 1/r gravitational potential energy versus time since the BB diagram upon a 1/r² P.E. versus time since the BB diagram for the whole universe, one sees that the curves cross over with the 1/r curve on top since 8 or 9 billion years ago when acceleration of the universe expansion rate is said to have begun. This diagramatic crossover point is when the 1/r 2-D potential energy again became capable of donating its energy to the 3-D 1/r² universe causing acceleration of its expansion rate. So, this HSBH G-field Dark Matter postulate can be extended to cover Dark Energy and it can even "predict" when Dark Energy should have become dominant. See http://GaryAKent.wordpress.com

[Gary Anthony]

This very interesting, would be keen to look at the paper, do you produce new solutions for spinning black holes?

I merely reiterate the Kerr metric with the caveat that reality does not end at the event horizon. Finite spin rate may be apparent at or above the event horizon but it cannot be measured when matter in-falls to below the EH to coalesce with the singularity. Kerr says a ring singularity may result. But, I say it must be a broad 2-D spacetime disk singularity. Maybe it's the same thing. But the idea that it must be so broad that it actually penetrates beyond the EH to the galactic periphery and even further is new.

Let's face it. Exotic Dark Matter will never be found. They have had enough time. Then, explanations like mine will be at a premium. My postulate may be part of the set of physical laws that could pertain to BH singularities. I do not understand how people can say with one breath that physics at extreme curvatures like at singularities is unknown and with the next breath claim to know enough to say that my postulate is impossible. Postulates are to be accepted at face value and tested against experiment or observation. Postulates do not need to be proven. My postulate explains the data. It predicts new data. It is unassailable mathematically. One cannot conclude anything else from the M-sigma relation and the anomalous stellar velocity dispersion.