See the post
The Hyperbolic Black Hole Galactic and Universe Gravitational Field
Below, after the following post.
The Hyperbolic Hyper-Massive Black-Hole Universe
The hyperbolic (declines as 1/r) black-hole galactic and universe gravitational field explains Dark Energy and Dark Matter.
Stephen Hawking did not buy his own pronouncements regarding the disappearance of information into black holes. Instead, as a retraction, he and some others invented a whole new theory of black-hole thermodynamics. So, in a sense, they concluded, the black-hole event horizon is a real surface. It is sometimes called a “quasi-surface”. However, the center of a black-hole is a physically real singularity. It is constrained only by the Heisenberg Uncertainty Principle.
There is no such thing as a valid theory of quantum gravity (how many papers are published in ArXiv on unicorns? By their standards, there should be dozens!) So, any appeal to QG to put the Kibosh on black-hole singularities is therefore bogus.
See The Hyperbolic Hyper-Massive Black-Hole Universe and Galactic Gravitational Field (HHBF), which is a paper written for the blog https://garyakent.wordpress.com that describes the e-Model for inflationary expansion of the universe. The hyperbolic hyper-massive black-hole gravitational field is a phenomenological postulate, that is, it is a tentative premise that should be confirmed by experiment or observation and need not wait for theoretical justification. In the case of galaxies and galactic clusters, there is already enough observational support for the galactic hyperbolic super-massive black-hole gravitational field (HSBF).
The point is emphasized that Birkhoff’s Theorem and other interpretive principles derived from general relativity cannot apply to any real black-holes. These rules presume that the massive bodies that are considered are always “unperturbed” and are perfectly “spherically symmetric”. No real black hole meets these criteria. The rules are good only for approximate calculation, not for “precision cosmology”.
Besides, GR should not prohibit a gravitational field that declines as 1/r if a metric is found, similar to the Schwarzschild metric, using assumptions and boundary conditions wherein a singular black-hole is presumed at the outset. If such a gravitational field can be confirmed, the e-model will serve as more evidence for the existence of our universe as part of a multiverse in meta-time.
Hugh Everett may one day be seen as a thinker on a par with A. Einstein. And, John Archibald Wheeler’s suggestion concerning the quantum self-interference of probability density waves may be taken more seriously while Everett’s declaration of the “reality of probability” as a sort of substance gains credence. Self-interference can explain the virtual absence of antimatter (AM) in our universe. AM would be confined to our virtual twin, which must exist according to the logical extension of Alan Guth’s inflation hypothesis wherein a virtual particle came into existence from a hyper-excited false vacuum which came to exist precisely because of its ultra-high energy level. It would be seen as the deeper mechanism behind apparent “symmetry breaking” and unbalanced annihilation of fundamental sub-nuclear particles and antiparticles to give our universe with matter as the dominant form.
The existence of an interference twin could also be helpful in explaining the hyperbolic field as the resultant of a superposition of states. As the real expression of a statistical process within the multiverse, we experience only the total sum, the superposed probability density form from which emerges probability, P —> 1. There are ways that such a superposition might affect the shape of a gravitational potential well. Gravity itself may be viewed as a probability vortex or wave in the Einstein Aether. There is much that has not been considered.
The hyperbolic black-hole gravitational field produces the mathematical result that the velocity distribution of stars in galaxies and galaxies in clusters follows the relation v =(GM)^1/2 and the gravitational potential energy follows P.E. proportional to ln(r), the natural logarithm of the radial distance from a black-hole or from the barycenter of several black holes. This is exactly the same as that predicted by hypotheses of “Dark Matter”. The hyperbolic black-hole gravitational field IS Dark Matter.
A naive interpretation of general relativity says that radiant energy like light, magnetic, electric or gravitational flux must decline as 1/r^(n-1) where r is the radial distance. Since our universe is apparently 3-D, having 3 spatial dimensions, such quantities should decline as 1/r^2. A less naive interpretation would have us find a new metric that satisfies GR but allows a decline in the gravitational force as 1/r, a hyperbolic decline, not parabolic or “exponential”, 1/r^2.
One way to do this is to choose a different coordinate system. We could choose a 2-D coordinate system. This 2-D surface would not necessarily be Euclidean. In fact, it might be hyperbolic. Then, a hyperbolic 1/r decline in gravitational strength would be not only possible, but required. But, it would be required only for black-holes.
After all, a black-hole has an event horizon that is called a “quasi-surface” because the entropy represented by all objects, including photons, that fall into a black hole is preserved on the “event surface”, a 2-D representation of the entire universe (potentially, by extrapolation of the concept). If a 3-D gravitational field could be reflected in the event surface, its image would be as a 2-D entity. Since nothing, not even light, can exit a black-hole, then neither should gravity be able to do so except by reflection in the event surface from external regions. It could get there initially because a black-hole must grow from a less massive form when it did not possess an event surface.
Another equivalent way to say this is that the 2-D overlay represents a state of the universe and the reality that we experience is a superposition of states, a linear sum of states each represented by their own equations of state in GR. The experience of quantum states is always of the sum of states. We never can sense individual component states.
Since the multiverse can have an infinite number of components, if the 2-D overlay could be composed of a virtually infinite number of 2-D sub-states, say, one for each orbiting body, however such a body and its orbit may be oriented, then so be it.