#93 Comparison diagram of the gravitational potential energy of a black hole versus an equivalent mass ordi...

SextonBlake, on 06 January 2012 - 08:10 AM, said:

"Some thoughts: Why should the material inside a black hole be a point mass? We have no evidence that fundamental particles like electrons and quark can break down. And we have neutrons in neutron stars with an escape velocity of 2/3 c. A point mass suggests a one dimensional dot, so it would not spin, and we know that all black holes do spin."

Well, Karl Schwartzschild’s analysis of general relativity results is the Schwartzschild metric which has solutions that proceed toward infinity at the event horizon and at the center of a black hole. He defines the event horizon by the singularity that he finds at the “Schwartzchild radius”. Kretschmann’s invariant results from an analysis that shows that the singularity at the event horizon is an artifact of poor coordinate choice, but the singularity at the center is real and not an artifact of coordinate selection. It is independent of coordinates and is therefore called an “invariant”. He showed that by “real” he means that for all intents and purposes the singularity, as a singularity, is probably infinitely deep and infinitely dense. But, we cannot actually measure it this way because Heisenberg’s Uncertainty will intervene.

Perhaps a one dimensional dot cannot spin, but the space immediately around it can. This space is filled with the intense (approaching infinite) gravitational field which can spin. It can spin relativistically too, i.e. “frame dragging”. The North and South poles on Earth are said to not spin (formally), but the rest of the Earth certainly does. The fact that an infinite depth in the gravitational field profile necessitates an asymptote is lost on many. That symmetry demands another asymptote as one proceeds toward larger radius is not recognized because Birkhoff’s Theorem and its congeners seem to prohibit it. Gravity must be “asymptotically flat”. That is, a hyperbolic gravity field is impossible.

But these are the results of interpretations of GR. It is not necessary to interpret it this way. If one desires, the right assumptions and boundary conditions can be selected that will permit a hyperbolic gravitational field. Perhaps one must drop a dimension and treat a black hole as a 2-D entity. This will certainly permit a 1/kr proportionality. Furthermore, such a hyperbolic gravitational field is renormalizable and the inverse square form is not. This unrenormalizability of inverse square gravity is what makes it impossible to merge gravity and quantum mechanics/dynamics. Inverse square gravity has a hyperbolic gravitational potential energy profile.

Quantum physicists love to renormalize infinities away. One way to do this arbitrarily for a black hole is to simply assign to the value of the gravitational strength at the center a finite quantity equal to 1 or whatever amount is appropriate for one’s purpose. This is the real mathematical meaning of “approaches infinity” anyway. It means larger than necessary to meet whatever stringent test one may apply. Setting quantities equal to 1 is S.O.P. and is often called invoking the “natural number system”. Trouble is, one cannot do this indiscriminately. The gravitational constant G and the speed of light cannot simultaneously be set equal to 1, for example. Infinite gravitational strength can be set equal to 1 or any arbitrary quantity but severe problems arise if one tries to set the hyperbolic inverse square potential energy profile at r = 0 equal to 1. So inverse square gravity is said to be "unrenormalizable".

The only point I really want to emphasize is that it would be worth it to admit the hyperbolic 1/kr supermassive black hole galactic gravitational field as a postulate. It leads to the conclusion that all the phenomena ascribed to Dark Matter can better be explained by this expedient.

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