Black Holes

[Gary Anthony]

Black-Holes:

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 Garyakent's Blog 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®, 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/r². 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/r².

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.

We may say that quantum mechanics/dynamics may be applied wholesale and directly to the whole universe and especially to black holes, while leaving GR completely intact. This is the implication of Alan Guth's Inflation Theory.

They say that quantum cannot handle a gravitational field because gravity is not "renormalizable". But, a hyperbolic gravitational field that declines as 1/r is, in fact, renormalizable. Except for the whole universe and for black holes, where we treat hyperbolic fields, we never have to deal with exponential 1/r² gravity fields as a whole anyway.

If necessary, we could play tricks like embedding a hyperbolic field inside another, so that F = (GMm/r)(1/r) and treating it as a linear quantum sum of states . Multiplication is fundamentally a summation process, after all. Maybe this would be expressed as an infinite series of some sort. The author will check on this and report in a future post.

Since the multiverse can have an infinite number of components, if the 2-D overlay (on the whole universe within the metaverse or on a black-hole) should 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.

One cannot get around the fact that the anomalous galactic cluster and stellar velocity distribution is observed to be v = (GM)^1/2, a constant, and orbital acceleration a® = GM/r. These can only be the pure mathematical result of hyperbolic F = GMm/kr where k = 1m (S.I. system) for dimensional integrity.

[Capricorn]

Is this plagerism or copyright infringement ?

[acey]

How does the 1/r theory account for the observed success of Newton's inverse square law in predicting planetary orbits etc, or general relativity in predicting phenomena such as precession of Mercury, etc. What does the 1/r theory predict for those situations?

[Gary Anthony]

Is this plagerism or copyright infringement ?

What in the world do you mean?

[Gary Anthony]

How does the 1/r theory account for the observed success of Newton's inverse square law in predicting planetary orbits etc, or general relativity in predicting phenomena such as precession of Mercury, etc. What does the 1/r theory predict for those situations?

The 1/r gravitational form requires a black-hole singularity and leaves Newton intact. In fact it is a Newtonian form because

F = GMm/kr, where k = 1m (or the unit vector of whatever unit system one wishes) so the dimensionality is exactly the same as Newton's law.

According to general relativity, this form is what Newton would be in a 2-D universe. It would be hyperbolic. The fact that black-holes follow a hyperbolic gravitational law, as attested to by observations, implies that they are 2-D entities in some way, shape or form.

The so-called "quasi-surface" of the spherical black-hole event horizon is a 2-D entity. The 2-D gravitational field potential energy is uniformly higher than the equivalent mass 3-D inverse square potential energy. See Garyakent's Blog and the image series at Gak's Fotothing . So, the matter/energy in-fall to a black hole is transformed not merely to an entropy contribution to the event surface, but to a increment in the higher energy 2-D field.

A 2-D field could be overlain upon our 3-D universe without contradiction. It might be visualized as a cylindrical field, rather like the "cylinders" of a computer hard drive. It may actually be very difficult to imagine a completely proper way to visualize it.

In a multiverse, the 2-D field may be a linear sum of 2-D field states, at least one for each orbiting massive body, regardless of the orientation of it or its orbit. Then, the 2-D field will amount to the so-called Dark Matter "halo" of gravitational attraction that is said to exist around galaxies that accounts for orbital acceleration, a® = GM/r and velocity, v = (GM)^1/2. These observational results or phenomenological summaries can be derived from the assumption of a hyperbolic field as given above.

The suggestion of a hyperbolic gravitational field was made at least a decade ago when Michael Rowan-Robinson mentioned it in a paper listed on ArXiv not long after the announcement of the acceleration of Hubble expansion in 1998. So, this is not really my idea at all. But, I am afraid that it is being forgotten and is not being adequately considered.

[acey]

F = GMm/kr is dimensionally inconsistent, unless you're redefining G.

I repeat my question: how do you explain the observed planetary orbits (and more generally, Kepler's Laws) which follow from a 1/r^2 force, not from 1/r?

Are you proposing to modify the inverse-square law with an extra 1/r term? Can you give a link to the Rowan-Robinson paper?

[Disco]

If black holes are your interest Yale University (Charles Bailyn) has released a lecture and notes on iTunes u and it is free!

Ps And on matters of a high brow nature I feel like chicken tonight.

[Gary Anthony]

F = GMm/kr is dimensionally inconsistent, unless you're redefining G.

I repeat my question: how do you explain the observed planetary orbits (and more generally, Kepler's Laws) which follow from a 1/r^2 force, not from 1/r?

Are you proposing to modify the inverse-square law with an extra 1/r term? Can you give a link to the Rowan-Robinson paper?

The hyperbolic gravitational field applies only to gravitational singularities of the kind found in black-holes. The gravitational fields of galaxies do not follow Kepler's laws or Newton. This is why "Dark Matter" was invented.

DM was meant to account for the anomalous stellar velocity distributions in galaxies and galactic velocity distributions in clusters and super-clusters. Dark Matter was meant to be an alternative to Mordechai Milgrom's MOND theory which was indeed formulated to be a modification of Newton's law.

But, the hyperbolic black-hole gravitational field (HBHF) leaves Newton completely intact. The HBHF is required only when considering galaxies or clusters that may have embedded black-holes. One would have to consider the anomalous velocity distributions in such cases anyway. The mathematical forms for orbital v and for a® imply the HBHF.

Newton's law for planetary systems and general relativity's explanation of the precession of Mercury are unaffected.

[acey]

Are you familiar with Bertrand's theorem? It states that the only central forces capable of producing stable closed orbits are ones proportional to 1/r^2 or r. A 1/r force cannot produce stable closed orbits. In your theory it would be impossible to orbit a black hole. But that's what stars in galaxies appear to be doing.

[Grunthos]

Gary

Is your original post an extension of the thread you started here on The Science Forum.com (back in Sep 2011)?

Or a similar post on physicsforums.com

Or another related one on absoluteastronomy.com ?

Just trying to work out the context of your "enquiries"

[Gary Anthony]

Gary

Is your original post an extension of the thread you started here on The Science Forum.com (back in Sep 2011)?

Or a similar post on physicsforums.com

Or another related one on absoluteastronomy.com ?

Just trying to work out the context of your "enquiries"

Yes. I post on a number of different forums.

[Gary Anthony]

Are you familiar with Bertrand's theorem? It states that the only central forces capable of producing stable closed orbits are ones proportional to 1/r^2 or r. A 1/r force cannot produce stable closed orbits. In your theory it would be impossible to orbit a black hole. But that's what stars in galaxies appear to be doing.

Stars orbiting supermassive black holes in the nuclei of galaxies are not in stable orbits and they do not return to the exact same position upon orbit (their orbits are not "closed"). So, they do not follow Bertrand's theorem.

All stars in all galaxies containing embedded black holes spiral inward and will eventually be swallowed up by the black hole(s). The only reason that galaxies with super-massive black holes are not termed "active" galaxies is that these black holes are so huge that their gravitational strengths decline over a so much larger circumference that the gradient is much less. So, stars are not torn apart by tidal forces. They are swallowed "whole" and are not chewed up. It is all so much more tidy. Little or no energy is lost in formation of "jets", for instance.

I do not think any real system meets the criteria of Bertrand's theorem. All such theorems exist only on paper and are always regarded as ideal. As idealizations, they are adequate only for approximate calculations, not for "precision cosmology".

You can see by the shape of spiral galaxies that they do not follow Newton's law, which would have v = (GM/r)^1/2 for orbital velocities. But, it is observed that, in fact, v = (GM)^1/2, a constant. If v continued to decline as r increases, then v ---> 0 near the periphery. The spiral arms of a galaxy would wrap all the way around the galactic center several times, like the mainspring of an old wind-up alarm clock. This is not what we see.

Since v becomes constant at and beyond the periphery, the spiral arms do not wrap around nearly as far and so, spiral galaxies exhibit the familiar pinwheel structures. The fact that v = (GM)^1/2 can be derived from the hyperbolic gravitational field F = GMm/kr, where k = 1m (the unit vector in S.I., or whatever unit system one desires), for dimensional integrity.

The math and observations say that the gravitational field around black holes is hyperbolic.

A hyperbolic black hole gravitational field explains all the phenomena that are now attributed to Dark Matter. Since the hyperbolic gravitational field potential energy is uniformly higher for an equivalent mass, it embodies more energy and thus it represents more mass according to E = mc^2. The hyperbolic black hole gravitational field IS Dark Matter.

Furthermore, The masses of supermassive black holes should be determined using F = GMm/kr not F = GMm/r^2. The difference in masses found this way winds up in the hyperbolic field itself and helps it mimic Dark Matter.

[acey]

OK, all you need to do now is explain why the field around a black hole is 1/r, not 1/r^2 as follows from general relativity.

[Gary Anthony]

OK, all you need to do now is explain why the field around a black hole is 1/r, not 1/r^2 as follows from general relativity.

Well, it does not follow from GR if black holes are fundamentally 2-D objects in some sense, just as one would not have expected that the event horizon would have defined a 2-D quasi-surface or "event sphere". Nor would one expect that there could be numerous 2-D overlays or black hole gravitational states lain upon our world to give a simulation of a 3-D entity.

In two dimensions gravity must be hyperbolic in nature. Why? Because it is 2-D.

The math and the observations are demanding. They describe a hyperbolic black hole gravitational field (HBHF). This HBHF is responsible for Dark Matter. And, the concept can be extended to the entire universe too, whereupon it can be seen to account for Dark Energy as well.

[JulianO]

Stars orbiting supermassive black holes in the nuclei of galaxies are not in stable orbits and they do not return to the exact same position upon orbit (their orbits are not "closed"). So, they do not follow Bertrand's theorem.

Do you have evidence from this? Does it apply to stellar mass black holes?

[acey]

In two dimensions gravity must be hyperbolic in nature. Why? Because it is 2-D.

The math and the observations are demanding.

I suggest you write it up as a paper and send it to a refereed journal. I'll look forward to seeing it when it's published.

[Grunthos]

I suggest you write it up as a paper and send it to a refereed journal. I'll look forward to seeing it when it's published.

My thoughts exactly.

A peer reviewed published paper would do wonders for the credibility of your hypothesis (although, tbh, I wouldn't be making any plane reservations for Stockholm yet...)

[acey]

Couple of things I'll look out for in the paper:

Why are black holes 2D?

How do you get round the fact that you can only have a 2-dimensional black hole if there is negative cosmological constant (i.e. BTZ solutions)?

Don't tell me now - I'll wait for the paper.

[Gary Anthony]

Do you have evidence from this? Does it apply to stellar mass black holes?

My evidence is the same as the evidence used by M. Milgrom to advance his theory of MOND. From observation, he deduces orbital acceleration a® = GM/r and orbital velocity levels off at v = (GM)^1/2. But, these are quantities that would be derived from F = GMm/kr, the hyperbolic field.

Why try to change Newton when a better solution is so simple?

This hypothesis would apply to any black hole that has a singularity at its core. It depends on this singularity in order to geometrically imply the hyperbolic field. In a gravitational strength diagram, an infinitely deep gravitational well implies an asymptote near the vertical axis. By symmetry, there must be an asymptote near the horizontal axis too. This is a hyperbola.

Birkhoff's Theorem and other rules like it do not apply because they are formulated only for perfectly spherical, unperturbed black holes and other massive bodies. But, in order to get an hyperbolic 1/r field out of GR, one might have to find a metric in only two dimensions because GR may imply that F is proportional to 1/r^(n-1) where n = number of spatial dimensions.

Astrophysicists and cosmologists will resist this idea because it implies that there is a 2-D overlay upon our universe, that is, we are part of a multiverse (with an infinite number of such 2-D overlays). We experience only the superposition, the linear sum, of these quantum gravitational states. So, in addition, admission of the hyperbolic black hole gravitational field would admit that quantum theory may be applied directly to the whole universe, just like GR. Then, quantum and GR must be regarded as two sides to the same coin.

Then, the search for a unified field theory or TOE is futile. All their funding will dry up. Hundreds of graduate students will be left without support, unless their professors scramble to submit new proposals ASAP.

They are not prepared to make this admission just yet. But, if Alan Guth's hypothesis of inflation stemming from a virtual inflaton particle in a hyper-excited inflationary quantum field in the false vacuum holds up, it means that the universe was once a quantum entity. Then, it still is.

Then, there is the math and observations that say the gravitational field around a black hole is hyperbolic.

See Garyakent's Blog .

[Gary Anthony]

I suggest you write it up as a paper and send it to a refereed journal. I'll look forward to seeing it when it's published.

I need a collaborator to help me analyze GR for a 2-D metric that will admit a hyperbolic field. I am studying GR now, but I am not yet proficient enough to fearlessly submit calculations for peer review. A collaborator would speed things up.

[Gary Anthony]

My thoughts exactly.

A peer reviewed published paper would do wonders for the credibility of your hypothesis (although, tbh, I wouldn't be making any plane reservations for Stockholm yet...)

It is not my idea anyway. Michael Rowan-Robinson reported that he attended a colloquium where a lecturer mentioned the idea. But MRR did not elaborate.

[acey]

I need a collaborator to help me analyze GR for a 2-D metric that will admit a hyperbolic field. I am studying GR now, but I am not yet proficient enough to fearlessly submit calculations for peer review. A collaborator would speed things up.

It has been proved some time ago that what you are trying to do is impossible. General relativity in 2 space dimensions has no Newtonian limit. Black hole solutions in 2 space dimensions are possible only if the cosmological constant is negative. Good luck with your studies.

http://arxiv.org/pdf/hep-th/9204099v3.pdf

[1001.5227] Geometry and observables in (2+1)-gravity

Phys. Rev. D 43, 2555 (1991): Gravitation in 2+1 dimensions

[Gary Anthony]

I am thinking of establishing a model for the universe wherein there is a 2-D "overlay" upon our 3-D world. There would be at least one overlay for each black hole. The universe would still be of a 3-D nature but it would have another layer of complexity.

Cosmologists do not seem to want to have anything to do with Hugh Everett or to consider anything that implies a multiverse. But, the mathematics and the data imply a hyperbolic gravitational field for galactic black holes. It seems that the hyperbolic field can exist only in a 2-D spacetime. But, this is a 3-D universe. So such a 2-D field must exist as a superposition, a quantum state that we experience only as a sum of states in a multiverse.