Event Horizons - Holographic Principle

[.Scott]

Another thread (now closed), got me thinking about the holographic principle. So I looked it up and found a couple of surprises. First it seems to be attached in some peculiar way to string theory. Second, it seems to be applied more restrictively than it I thought. It's especially that second item that I have a questions about.

So I will describe things as I understand them and let the accomplished physicists on this forum reform, revise, and/or destroy it.

First, whenever I think of event horizons, I consider the ones generated from an accelerating reference frame as well as those hiding black holes. And so I tend to view them as artifacts of the reference frame rather than something inherent to a black hole. The event horizon of a black hole is special only in that it is shared by a wide range of reference frames - in fact, almost all of the possible reference frames external to it.

So the notion that all of the information from the raw materials that went into the formation of the black hole is present on the horizon begs the question of how it gets there. For material than enters the black hole after its formation, the answer is simple: in the reference frame of an outside observer, the material never penetrates the horizon. This is also true of event horizons that trail accelerating reference frames.

But what about the material that's behind the event horizon (black hole or accelerating reference frame) when it formed? How does it's information reach the event horizon? Since an event horizon is the an artifact of the reference frame, I reason that the inability of the BH event horizon to hide the information stemmed from the information already being at the event horizon when it formed. And since event horizons are artifacts of reference frames, that information must be available everywhere an event horizon may be described.

So describe any sphere around any object or set of objects and, in principle, the information available at the sphere is sufficient to describe the objects within it - and perhaps even beyond it. Similarly, describe any accelerating reference frame, and the hyperbolic event horizon it leaves in its wake must also contain all of the information trailing that horizon.

But the descriptions I read about the holographic principle don't seem to go that far. They suggest that the information for the entire content enclosed by the Cosmological Horizon may be available at the Cosmological Horizon, but do not generalize this to any sphere.

So, do I go to far?

 

[jedishrfu]

Susskind talks about it here " The World as a Hologram":

 

[PeterDonis]

whenever I think of event horizons, I consider the ones generated from an accelerating reference frame as well as those hiding black holes. And so I tend to view them as artifacts of the reference frame rather than something inherent to a black hole.

This is not a good way to look at it. The Rindler horizon (the one that arises because of acceleration in flat spacetime) has some properties in common with the event horizon of a black hole, but it differs in a crucial respect: a Rindler horizon is observer-dependent, while the event horizon of a black hole is not. The event horizon of a black hole is a global property of the spacetime geometry.

The rest of your reasoning simply builds on this mistake.

 

[.Scott]

This is not a good way to look at it. The Rindler horizon (the one that arises because of acceleration in flat spacetime) has some properties in common with the event horizon of a black hole, but it differs in a crucial respect: a Rindler horizon is observer-dependent, while the event horizon of a black hole is not. The event horizon of a black hole is a global property of the spacetime geometry.

The event horizon for a black hole is also observer dependent. For someone dropping into the black hole, there is no event horizon - at least not where it appears for observers at a distance. So the BH horizon is only "global" because the reference frames which share the horizon are global. But the local spacetime geometry of any segment of the BH horizon is not different from the local spacetime geometry of any segment of a Rindler horizon.

Or, if it is, why would you think so?

The rest of your reasoning simply builds on this mistake.

Actually, the core part of the reasoning does not rely on Rindler horizons. When a black hole forms, there needs to be a mechanism for its event horizon to immediately contain all information about its content. The horizon "generator" you described in another thread describes a shell arising from the center of a star to meet the newly formed BH event horizon. But it is almost as if that shell collects all the internal stellar information along its way and deposits onto the new surface - just before that information would have been lost forever.

In any case, you have a choice: either the information on any sphere always contains all the information from its interior. Or somehow that information is collect and transported to the surface at or leading up to the genesis of a black hole.
I think it would be a tough argument to say that it collects there only under BH genesis conditions - since those are exactly the conditions when transporting that information would be most difficult to the extreme.

Now, having said that, why would it not be extended to Rindler horizons?

 

[PeterDonis]

The event horizon for a black hole is also observer dependent. For someone dropping into the black hole, there is no event horizon

This is not correct. The event horizon is just what I said, a global feature of the spacetime geometry.

The horizon "generator" you described in another thread describes a shell arising from the center of a star to meet the newly formed BH event horizon.

No, the surface formed by the horizon generators is the event horizon. The horizon is not "newly formed" when the surface of the collapsing matter passes through it. It was already there, formed by the generators as I described.

it is almost as if that shell collects all the internal stellar information along its way and deposits onto the new surface

This is a speculation connected with the holographic principle. It is not part of standard classical GR.

In any case, you have a choice: either the information on any sphere always contains all the information from its interior. Or somehow that information is collect and transported to the surface at or leading up to the genesis of a black hole.

Or the whole premise of the holographic principle is wrong to begin with. None of this is part of classical GR.

 

[.Scott]

Susskind talks about it here " The World as a Hologram"

Thanks for the link.
I listened to all of it. I noticed that the link to String Theory is pretty light. The discussion shows that the Holographic Principle meshes with String Theory - not that it is in any way dependent on it.

It also shows that, in claiming that the information about the content of a shell is always available at the shell, I am going only slightly further than Susskin. There were two places in the video where he almost says that (44:20 and 47:35). It's not even clear whether he intended to suggest this or not.

I also like his discussion towards the end (53:55) where he asks about the properties of the cosmological horizon. The notion that information about what is beyond that horizon is encoded in that surface as well.

 

[.Scott]

The event horizon is just what I said, a global feature of the spacetime geometry.

Is it your view that someone falling through a BH event horizon would be affected by that crossing - more than crossing a Rindler Horizon? Would you claim that there would be no elevated temperature at a Rindler Horizon? I don't doubt that a BH event horizon is a feature of the global BH spacetime geometry. But it seems to me that all event horizons share the same local characteristics.

No, the surface formed by the horizon generators is the event horizon. The horizon is not "newly formed" when the surface of the collapsing matter passes through it. It was already there, formed by the generators as I described.

Ahhh. I think I understand. But initially, that horizon generator shell is only a moving boundary - just like any other set of photons radiating from a small source. And the boundary actually does contain photons - but only as viewed by an outside observer. Is that it?

Or the whole premise of the holographic principle is wrong to begin with. None of this is part of classical GR.

Okay. But given the holographic principle, complete information about the interior of any sphere must exist at the surface of the sphere.

I didn't realize you considered the holographic principle so disposable.
What is your assessment of the holographic principle? Is it on par with GR? Far from it? Or not even worth the discussion?

 

[PeterDonis]

Is it your view that someone falling through a BH event horizon would be affected by that crossing

No. But the fact that the event horizon is a global feature of the spacetime geometry in a BH spacetime does not require that an infalling observer notice anything unusual locally when he crosses it.

This is all very basic GR, so I'm wondering where you are getting your understanding of black holes from.

Would you claim that there would be no elevated temperature at a Rindler Horizon?

This is the relativity forum so we are talking about classical GR, in which there is no such thing as "temperature" associated with a black hole horizon, or any horizon.

If you include quantum effects, then there is Hawking radiation associated with a black hole horizon, and Unruh radiation associated with a Rindler horizon, and the two phenomena are very similar. But discussion of that really belongs in the quantum forum since these are quantum effects.

initially, that horizon generator shell is only a moving boundary - just like any other set of photons radiating from a small source.

The horizon is always a "moving boundary" in any sense of "moving" that is not coordinate dependent. Observers falling through the horizon always see it as an outgoing lightlike surface--i.e., moving at the speed of light relative to them.

The invariant concept you might be trying to capture here is that, prior to the surface of the collapsing object intersecting the horizon, the surface area of the horizon is increasing (but even here you have to be careful how you define "surface area" and "increasing"), but it stops increasing at the instant the surface of the collapsing object passes through it.

the boundary actually does contain photons - but only as viewed by an outside observer. Is that it?

No. Whether the generators of the horizon correspond to actual worldlines of actual photons depends on whether actual photons are actually emitted. But the null curves that are the generators can be defined whether or not actual photons are following them.

If actual photons are following the generator curves, then that is true for all observers; it's an invariant.

What is your assessment of the holographic principle? Is it on par with GR?

Certainly not. GR is an experimentally verified theory. The holographic principle is untested speculation.

 

[.Scott]

No. But the fact that the event horizon is a global feature of the spacetime geometry in a BH spacetime does not require that an infalling observer notice anything unusual locally when he crosses it.

This is all very basic GR, so I'm wondering where you are getting your understanding of black holes from.

A lot from Susskin, such as in the video. The reason I asked about "Alice" was because you strongly differentiated between BH and Rindler event horizons, and the notion that what should apply to one should also apply to the other. Since you didn't seem to see BH event horizons as dependent on the reference frame, I thought you might have a different view of "Alice".

This is the relativity forum so we are talking about classical GR, in which there is no such thing as "temperature" associated with a black hole horizon, or any horizon.

If you include quantum effects, then there is Hawking radiation associated with a black hole horizon, and Unruh radiation associated with a Rindler horizon, and the two phenomena are very similar. But discussion of that really belongs in the quantum forum since these are quantum effects.

OK. BH:GR; EH:QM. I will try to follow that line.

 

[PeterDonis]

A lot from Susskin, such as in the video.

I would strongly suggest taking some time to work through a standard GR textbook on black holes (Carroll's online lecture notes have a chapter on them, which is a good starting point) before trying to interpret any discussion of a highly advanced, speculative topic like the holographic principle.

The reason I asked about "Alice" was because you strongly differentiated between BH and Rindler event horizons

In some particular respects, yes. But I also said that there are other respects in which they are very similar. What an observer crossing them observes (or does not observe, which is more to the point) is one of the respects in which they are similar.

BH:GR; EH:QM

I'm not sure what this means. If "EH" stands for "Event Horizon", then that's GR, not QM.

 

[Tomas Vencl]

...
But what about the material that's behind the event horizon (black hole or accelerating reference frame) when it formed? How does it's information reach the event horizon? Since an event horizon is the an artifact of the reference frame, I reason that the inability of the BH event horizon to hide the information stemmed from the information already being at the event horizon when it formed. And since event horizons are artifacts of reference frames, that information must be available everywhere an event horizon may be described...
...

I can be completely wrong, I do not meet "A" level, but next image can illustrate basic idea about forming BH.
This is at rest distant observer "view" to forming BH from 3 shells (transparent for signals). y-axis is Schwarzschild coordinate time, and x-axis is r (I realize that Schw. coordinates are not used fully correctly).
The shells (dark blue, the magenta is their proper time) are collapsing to the center. At the centre of incoming BH is signal (30 light pulses) generator. Outcoming light pulses are red. Schwarzschild radius is outer light blue vertical line. Picture shows, how the shells are "frozen" for distant observer during BH forming. Also there is last finite signal which can escape, the next are trapped in BH. This is generating of horizon. As you see, outgoing signal from the centre is more and more redshifted, but outside still can be information about the centre, or better say, you can always "see" the past of the centre. As well as the other regions inside BH, but only their past.

 

[PeterDonis]

next image can illustrate basic idea about forming BH

This is the same issue that has already been discussed: your diagram uses Schwarzschild coordinates, and the conclusions you are drawing from it are coordinate-dependent. Try drawing a similar diagram in Lemaitre (or Painleve) coordinates; it will look very, very different.

 

[Tomas Vencl]

Yes, I agree and I hope I am not in contradiction with you. I only wanted to show how it looks for distance observer at rest, and any other coclusions I am not doing. I know that for comoving coordinates the 2M singularity vanish. ( In the calculation is many simplifications, one of them stop the computing before magenta trajectory (propper time) reach the centre, this is only calculation fault, those are also not comparable and are misleading, I had to delete them)
But generally it seems to me that model has similar results to Oppenheimer-Snyder solution here:
https://www.researchgate.net/publication/322440977_On_the_consistency_of_the_Oppenheimer-Snyder_solution_for_a_dust_star_Reply_to_Marshall%27s_criticism

 

[PeterDonis]

I only wanted to show how it looks for distance observer at rest

But that's the problem: "how it looks" is not an invariant, it depends on your choice of coordinates.

generally it seems to me that model has similar results to Oppenheimer-Snyder solution

Not once you get near, at, or beneath the horizon. That's the point.

 

[PeterDonis]

here

On a quick skim, this paper seems to be making the same error that has already been described in this thread: mistaking coordinate-dependent quantities for invariant properties of the spacetime geometry.

 

[.Scott]

On a quick skim, this paper seems to be making the same error that has already been described in this thread: mistaking coordinate-dependent quantities for invariant properties of the spacetime geometry.

I don't think anyone is making that mistake. We may not understand everything as well as you, but we all know that space-time in the neighborhood of a BH has extreme invariant geometries.

I think the problem may lie in semantics. My guess is that you are using the term "event horizon" to mark an invariant space-time boundary. Where as I (and some others) are using it to designate a boundary where extreme time dilation and associated effects are observed.

You agree that Alice can fall through that space-time boundary without affect. But would you also say that she does not see an event horizon as she passes through it - because the event horizon isn't there? I would. And by using those semantics I can go on to ask if Alice sees an event horizon at all - at some other location either in front of her or behind her.

By using what I believe are your semantics, how would one ask that question?

 

[PeterDonis]

I don't think anyone is making that mistake.

Then you are mistaken. See below.

we all know that space-time in the neighborhood of a BH has extreme invariant geometries.

What does "extreme invariant geometries" mean? If you mean spacetime curvature is extreme, that's not correct, at least not for black holes of stellar mass or larger. Spacetime curvature at the horizon of such holes is still weak.

My guess is that you are using the term "event horizon" to mark an invariant space-time boundary.

Well, yes, of course, since that's the meaning of the term "event horizon" in the GR literature. If you're using that term to mean anything else, you're using it wrong.

You agree that Alice can fall through that space-time boundary without affect

Without noticing anything different from passing through any other lightlike surface, yes. She will notice gradually changing spacetime curvature as she falls, but, as noted above, spacetime curvature at the horizon of a stellar mass or larger black hole is still weak.

would you also say that she does not see an event horizon as she passes through it - because the event horizon isn't there? I would.

Then you are wrong. Please, go work through a GR textbook and learn the proper invariant definition of an event horizon. You are getting close to a warning at this point.

By using what I believe are your semantics, how would one ask that question?

You can't, since the event horizon is invariant and is there for all observers. However, that does not mean Alice can tell, locally, exactly when she crosses the horizon. She can't. The reason is that the event horizon is a globally defined concept: it is the boundary of the region of spacetime (the black hole) that cannot send light signals out to future null infinity. The only way to know for sure exactly where that boundary is, is to know the entire future of the spacetime; and Alice can't know that.

 

[PAllen]

I compute that curvature is pretty large well outside the horizin of a stellar mass BH, e.g. tidal stretching of a one meter infalling body would reach ten thousand g of tension several kilometers outside the horizon. This was a quick calculation, but generally my understanding is that matter is tidally shredded well outside a stellar mass BH.

 

[DrGreg]

I think the problem may lie in semantics. My guess is that you are using the term "event horizon" to mark an invariant space-time boundary. Where as I (and some others) are using it to designate a boundary where extreme time dilation and associated effects are observed.

There are several types of "horizon".

A black hole's event horizon is sometimes called an "absolute horizon", the boundary of a region from which light can't escape to infinity. That's a coordinate-independent definition. For almost all authors (I think), "event horizon" means the same thing as "absolute horizon".

There is also a notion of "apparent horizon", loosely speaking the boundary of a region from which light can't travel "outward". "Outward" is a coordinate-dependent concept. A black hole's event horizon is also an apparent horizon in Schwarzschild coordinates, but not in some other coordinates e.g. Kruskal coordinates. In flat spacetime a Rindler horizon is an apparent horizon in Rindler coordinates, but not in Minkowski coordinates. There is "extreme ['gravitational'] time dilation" (as you put it) near a Schwarzschild apparent horizon and near a Rindler apparent horizon, but only in the appropriate coordinates. A freefalling observer would notice nothing different locally near either of these horizons using Kruskal or Minkowski coordinates respectively (according to classical theory).

(This is outside my area of expertise, but I think that the holographic principle is proposed for absolute horizons, not apparent horizons.)

 

[PeterDonis]

There is also a notion of "apparent horizon", loosely speaking the boundary of a region from which light can't travel "outward". "Outward" is a coordinate-dependent concept.

I agree that "outward" is coordinate-dependent, but I think it's worth going into a bit more detail about why. First I'll give the technical definition of an apparent horizon (the more technical term is "marginal outer trapping horizon"): it's a 3-surface foliated by 2-spheres on each of which the expansion of the congruence of radially outgoing null geodesics is zero. (Each such 2-sphere is called a "marginal outer trapped surface".) The reason it's coordinate-dependent is that which congruence of null geodesics is the "radially outgoing" one on a given 2-sphere depends on our choice of coordinates. However, that's not as much of a dependence as you might think; see further comments below.

Note that, even though the definition involves radially outgoing null geodesics on 2-spheres, the 3-surface itself (i.e., the horizon) does not have to be a null surface, and in fact won't be unless the spacetime exterior to the horizon is stationary (i.e., in idealized cases like Schwarzschild spacetime, but not a real hole that has things falling into it).

A black hole's event horizon is also an apparent horizon in Schwarzschild coordinates, but not in some other coordinates e.g. Kruskal coordinates.

I'm not sure if this is correct. The congruence of radially outgoing null geodesics at $r = 2M$ certainly looks different in spacetime diagrams in these charts, but I think it's the same congruence in both cases, and the expansion of a given congruence of null geodesics is an invariant; it doesn't depend on coordinates.

In flat spacetime a Rindler horizon is an apparent horizon in Rindler coordinates, but not in Minkowski coordinates.

I don't think this is correct either; the expansion of the congruence of null geodesics that forms the Rindler horizon is certainly not zero, and again, it's the same congruence in both coordinate charts, so I don't think the Rindler horizon is an apparent horizon in either case.

I think that the holographic principle is proposed for absolute horizons, not apparent horizons.

I think it depends on whose research you look at. I've seen some papers that strongly suggest that the details of how states of infalling objects get "recorded" at the horizon (so the information is preserved there) depend on properties of apparent horizons (marginal outer trapping horizons), not event horizons. The difference is that marginal outer trapped surfaces are locally detectable (just measure the expansion of the radially outgoing null geodesics), and any kind of mechanism for storing states at a horizon requires something local to be going on; the mechanism can't "know" the entire future of the spacetime, which is what it would need to know to know it's at an event horizon.

 

[PeterDonis]

I compute that curvature is pretty large well outside the horizin of a stellar mass BH, e.g. tidal stretching of a one meter infalling body would reach ten thousand g of tension several kilometers outside the horizon.

Yes, that's true; if we assume Alice is a normal human, she'll be shredded well outside the horizon of a stellar mass BH. But it is certainly possible to imagine materials that can withstand that level of tidal tension.