Galactic M-Sigma Relation And The Anomalous Stellar Velocity Dispersion

[G Anthony Kent]

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, it 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.

 

 

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/c², this difference represents mass – matter that is unseen and unseeable. That is, this is Dark Matter.

 

 

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

Edited June 1, 2012 by Gak