Does general relativity allow nested event horizons?
I have seen references of such, but they are beyond my comprehension. For example, see
http://nrumiano.free.fr/Estars/int_bh.html" [Broken] and
Hope they cover your question.
They seem to be a good resource on black holes, but a brief glance shows my question still remains unanswered.
I don't see why a horizon could not exist within a horizon, but I don't think I have read of that situation explicitly. How about a black hole in a closed universe?
According to the "holographic principle", there is no difference between something that exists within an event horizon, and something that exists on an event horizon, so "a horizon could not exist within a horizon" unless the two horizons coincide.
A closed universe is a black hole. So, although a black hole within a closed universe may seem like it is an example of one horizon within another horizon, these two horizons might actually coincide with one another.
AFAIK the holographic principle is consistent with GR, but it is not necessarily a part of it. In other words, the mass of a black hole (uncharged and nonrotating) is proportional to the radius of its event horizon rather than its enclosed volume so horizons apparently can't be nested. For example, if a large black hole swallowed a small black hole, the radius of the smaller horizon would simply be added to the larger horizon.
Isn't it the entropy of a black hole that is proportional to the area of the horizon?
So I observe a black hole (of which I am not a part), and simultaneously observe my universe (of which I am a part - closed for sake of argument). Are you telling me they are one and the same?
Is the "holographic principle" compatible with general relativity, say under quantum gravity?
That's right, so I changed "area" to "radius" above.
According to the holographic principle these two event horizons must coincide. This implies that all of physics must operate on an event horizon. This is according to the "holographic principle"...that doesn't mean that it's right, but it could be.
"www.arxiv.org/quant-ph/0311049"[/URL] a paper on "Black holes and information theory" with some discussion of its compatibility with GR and references to at least one other paper on quantum gravity.
I can see that all horizons may somehow be connected, but obviously occupy different spacetime - i. e., they are not equivalent.
Given arbitrary perspectives for an observer, all spacetime would eventually be included in a horizon.
If spatial density is constant there exists one event horizon, yet with variable density I would think that any combination of horizons could exist.
Your question was about nested event horizons: e.g., concentric spherical shells of declining radius. Starting with a first uncharged and nonrotating black hole of radius r_1 and a second uncharged and nonrotating black hole of radius r_2<r_1, if these two black holes are merged then what is produced is a third uncharged and nonrotating composite black hole of radius r_1+r_2; not a black hole of radius r_1 containing the other black hole as a nested concentric spherical shell. From the outside, this is all that we can say because we don't have access to any information about what is inside the event horizon of radius r_1+r_2.
Take the persective of an observer outside of and at rest with respect to the composite black hole in the example above; you have no information about what is going on inside the event horizon, only about what is on the event horizon. What is interesting about the holographic principle is that this may be all that we need to know; ultimately there may be no need to imagine that there is anything at all going on inside of this event horizon.
I'm not sure what you mean by "spatial density", but the idea is that it may be possible to model everything within any 3-D volume as existing only on a 2-D surface. In that case, then you could look at this either way: either there exists only one event horizon, or that there really are event horizons within event horizons.
By "nested" I meant "within" (as per the thread title), not necessarily concentric. The arguments about projection remain the same for me, though.
There is information about a black hole: charge, mass and spin.
If there is no information about a black hole, how do we know there is no horizon inside?
Any dimensional space can be projected, with a loss of information, upon any lesser-dimensional space.
One interesting outcome of a black hole being a 2-D spatial "holographic" projection of 3-D space is that charge, mass and spin are properties unaffected by the transformation.
Another is that a black hole may represent an event horizon of finite width (GM/c2, in the case of a Schwarzchild black hole), not infinitesimal.
Instead of "spatial density" I should have written "spatial mass-energy density."
That doesn't sound right.
(1) The holographic principle says there's enough information on the event horizon to describe what happens inside. It's a rather deep philosophical assertion to claim that there is no difference between a thing and the information describing it.
(2) So what if the information is on the horizon? The information on the event horizon that says "there's an event horizon here" and the information on the event horizon that says "there's an event horizon inside" are different pieces of information.
This is only information about what is on the event horizon, and not necessarily about what is going on inside the event horizon. From the outside, we can not observe anything whatsoever about what is going on inside of an event horizon.
An observer who is situated outside of an event horizon can not have any information about what is going on inside of the event horizon...that is what an event horizon is.
We don't, as I said:
What the thermodynamics of black holes teaches us is that there is no loss of information when the interior space of an event horizon is projected onto its surface.
It would be a philosophical assertion to claim knowledge about 'a thing' beyond the information describing it, and I am not making any such assertion.
They are different pieces of information, but they both fit on the event horizon.
This quote is also interesting in view of the holographic principle:
History effects on an event horizon.
Let me make a point on this subject, a black hole is a singularity in Einstein’s theory of relativity. The cause of the event horizon is the great curvature of space-time due to the mass of the black hole. As such, the space time itself is continuous across the event horizon. The event horizon is the point where the apparent gravitational force (as seen from outside the system) is so strong as to yield an escape velocity greater than the speed of light thus blocking any communications from the inside. Since we are talking about effects due to a singularity, the issue of being inside or outside the event horizon can be taken right down to the horizon itself.. From the perspective of a body falling through the event horizon the, horizon is the point where the tidal forces exceed any binding force capable of maintaining integrity of that body (of course, any anthropomorphic construct would be destroyed by tidal forces well before it reached the event horizon).
The interesting thing about the above is that the black hole itself is a singularity thus a black hole falling into another black hole (i.e., passing through the event horizon) is, being a singularity, unaffected by tidal forces. However, such an event can not be observed from the outside as it occurs within the event horizon of that second black hole (note that the same fact is true if the roles of the two black holes are reversed). It follows that there certainly could be more than one black hole inside any observed event horizon.
In fact, I made an interesting calculation on the total energy radiated by a charged point object falling into a black hole when I was a graduate student. The answer I obtained was E=mc^2 which implied all the mass was converted into radiation before the actual collision with the hole. And, since anything having a spatial structure would be destroyed by tidal forces before it could physically become part of the original black hole, only a point entity could merge with a black hole unless quantum tunneling is invoked.
The whole issue resolves down to the fact that space inside the event horizon could be a very complex construct indeed. In fact, the theoretical structure inside the event horizon could be a universe unto itself not necessarily containing that singularity supposedly at the core of the phenomena. All the existence of the event horizon requires is sufficient mass to provide the required curvature of space. For example, one could imagine a massive thin shell with insufficient mass density to yield an event horizon until the radius of interest included the entire shell (not that I am suggestion such a shell could exist).
What is important here is that it is the event horizon itself which removes the interior of the region from observation. All the conservation laws should hold across the boundary and certainly the external shape of the event horizon need not be spherical. It might be very interesting to see an exact GR correct calculation of the time evolution of the shape of two event horizons as they merged with a non zero relative angular momentum. I say “see” because I suspect that calculation has already been done years ago. Personally, I think a computer generated image of the event would be interesting to see. I have been out of touch with physics for some forty years so I am not the one to do it.
And, Eether, if you want to see a construction of the universe from information alone, take a look at http://home.jam.rr.com/dicksfiles/Explain/Explain.htm [Broken]. send me a private message if you are interested.
Have fun -- Dick.
What I want to see is a set of "alternative quantum fields and physical laws "painted" on a distant, vast surface":
Now am I suposed to take that seriously? :rofl: :rofl: Or, more seriously, do you?
Have fun -- Dick
Yes, it is meant to be taken seriously; and yes, I do take it very seriously. If you have an argument (or a published reference that you can cite) against it then I would like to see it.
Against it isn’t the issue. The issue is your interpretation of his "painted on a distant, vast surface”. A decent understanding of Holograms should convince you that viewing the quantum wave functions as analogous to light waves yields a mental image of the universe as a holographic construct. The result is set by the boundary conditions: completely equivalent to alternative quantum fields and physical laws "painted" on a distant, vast surface. It follows that what you would “like to see” is right in front of your eyes on a daily basis. And again, if you would like to see such a perspective logically defended look at my presentation, http://home.jam.rr.com/dicksfiles/Explain/Explain.htm [Broken]. If not, don’t worry about it; all it is nothing but a demonstration that any logical explanation of reality has such constraints on it. “There are a million stories in the naked city”; if they are internally consistent with all available information, “which one might be true is” - any one of them! :rofl: :rofl:
If his presentation is totally internally consistent, then it is fine and I would have no criticisms at all. In fact, if you really want to see such a thing (in your mental eye) check out a "simple geometric proof". A simple quantized representation of such a thing projects exactly the standard quantum solutions to all the physics problems I am aware of (and I can prove that). However, the proof is not trivial as the solution being represented is a many body solution consisting of all the bodies in the known universe.
Have fun -- Dick
No, I want to see something specific. I want to see someone start out with the FLRW line element + Einstein's field quations in spherical coordinates, drop the r coordinate, and then still predict the CMB temperature multipole anisotropies for example (preferably yielding some new knowledge, like an explanation of dark matter and energy, in the process).
Ok, I will look at this later.
Nested event horizons?
It depends upon what you mean by "nested", I guess. You can look at the block diagrams (aka "conformal diagrams" or "Carter-Penrose diagrams") in http://www.math.ucr.edu/home/baez/RelWWW/history.html [Broken] and decide if any of these satisfy your request. (I could give more examples but these will do to begin with.)
A black hole in a "closed" FRW universe (this potentially serious misleading terminology; you should say rather "FRW dust with spherical hyperslices orthogonal to the dust particles" or something similarly awkward but precise) certainly does NOT exhibit nested event horizons.
Note that the defining property of a black hole should probably be taken to be the existence of an event horizon (or a suitable variant of the classical and "teleological notion), rather than the existence of a singularity. The merger of two black holes then results in one black hole, not a pair of nested holes. See Hawking and Ellis, The Large Scale Structure of Space-Time.
This statement is seriously misleading; see http://www.math.ucr.edu/home/baez/physics/Relativity/BlackHoles/universe.html
Thank you Chris; I am trying to decipher the diagrams on the first site you offer. At first glance it seems that the answer to my question applied to the universe as we know it is "no." As to the eventual possibility for all spacetimes that nested horizons exist, the answer appears to be "yes." Maybe an example of the latter involves a suitable variation of cosmological constants.
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