# Holographic principle and entropy mapping of a BH

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## Main Question or Discussion Point

I've just started reading up on the holographic principle and eventually want to work my way to figuring out what Verlinde has proposed using it for. One thing I've noticed in a couple of papers is the mapping of the entropy of a black hole onto a holographic screen. Why are families of light rays considered for how the entropy is mapped to the screen? To me, it sounds like by introducing the light rays and the focusing theorem, we are talking about real physical photons mapping out the entropy, but that doesn't seem to make any sense since I haven't imagined the screen as a physical object.

We also know there exists orbits for photons around a BH, what is there to say about these paths? Would they simply not correspond to a point on the holograph that carries information about the BH? Or are these light rays simply tools to characterize the mappings?

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I've just started reading up on the holographic principle and eventually want to work my way to figuring out what Verlinde has proposed using it for. One thing I've noticed in a couple of papers is the mapping of the entropy of a black hole onto a holographic screen. Why are families of light rays considered for how the entropy is mapped to the screen? To me, it sounds like by introducing the light rays and the focusing theorem, we are talking about real physical photons mapping out the entropy, but that doesn't seem to make any sense since I haven't imagined the screen as a physical object.

We also know there exists orbits for photons around a BH, what is there to say about these paths? Would they simply not correspond to a point on the holograph that carries information about the BH? Or are these light rays simply tools to characterize the mappings?
Well... the boundary is the screen, so to get any information about it we'd want to get as close to the event horizon as we could. In practice, which is kind of what you're asking, I have no clue if that would be feasible, and I'm not sure that it matters for the purposes of the Holographic Principle. As I understand it, and my understanding is not deep, the answer to your last 3 sentences is... yes.

Yes, these paths exist, but I don't know what you mean, "what is there to say about them".

Now you clarify the point in your second query, and yes, to even measure this (given current "understanding") would require the ability to monitor the position of the EH, which means knowing when light ceases to have a chance at a round trip. That DOESN'T correspond to stable orbits however... that's entirely different. The HP is all about the EXACT event horizon: the boundary between light, and no light escaping. It's the fluctuations in this boundary that encodes the information in the principle.

for your third question, if not light... what?

JesseM
I've just started reading up on the holographic principle and eventually want to work my way to figuring out what Verlinde has proposed using it for. One thing I've noticed in a couple of papers is the mapping of the entropy of a black hole onto a holographic screen. Why are families of light rays considered for how the entropy is mapped to the screen? To me, it sounds like by introducing the light rays and the focusing theorem, we are talking about real physical photons mapping out the entropy, but that doesn't seem to make any sense since I haven't imagined the screen as a physical object.

We also know there exists orbits for photons around a BH, what is there to say about these paths? Would they simply not correspond to a point on the holograph that carries information about the BH? Or are these light rays simply tools to characterize the mappings?
Are you asking about the original Bekenstein bound which dealt only with a black hole event horizon, or about the more general bound proposed by Buosso (which nowadays seems to be called the 'covariant entropy bound') which can be defined for any spacelike surface where light rays emerging from it will converge? This type of bound is discussed in this article on the holographic principle by Jacob Bekenstein:
In 1999 Raphael Bousso, then at Stanford, proposed a modified holographic bound, which has since been found to work even in situations where the bounds we discussed earlier cannot be applied. Bousso's formulation starts with any suitable 2-D surface; it may be closed like a sphere or open like a sheet of paper. One then imagines a brief burst of light issuing simultaneously and perpendicularly from all over one side of the surface. The only demand is that the imaginary light rays are converging to start with. Light emitted from the inner surface of a spherical shell, for instance, satisfies that requirement. One then considers the entropy of the matter and radiation that these imaginary rays traverse, up to the points where they start crossing. Bousso conjectured that this entropy cannot exceed the entropy represented by the initial surface--one quarter of its area, measured in Planck areas. This is a different way of tallying up the entropy than that used in the original holographic bound. Bousso's bound refers not to the entropy of a region at one time but rather to the sum of entropies of locales at a variety of times: those that are "illuminated" by the light burst from the surface.
Some more details can be found in section 3 of this paper.

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Yes, these paths exist, but I don't know what you mean, "what is there to say about them".
The path that a photon would take from the screen to the orbit that would not fall into the BH, would this correspond to any entropy? Or should I be looking at this description as light emitted from the horizon going towards the screen maps entropy only?

nismaratwork said:
for your third question, if not light... what?
Why anything? With my extremely limited knowledge of what's going on here, it seems like the entropy being mapped to this screen is more of a mathematical concept.

Are you asking about the original Bekenstein bound which dealt only with a black hole event horizon, or about the more general bound proposed by Buosso (which nowadays seems to be called the 'covariant entropy bound') which can be defined for any spacelike surface where light rays emerging from it will converge? This type of bound is discussed in this article on the holographic principle by Jacob Bekenstein:

Some more details can be found in section 3 of this paper.
I'm looking at Bekenstein's bound. I've heard of this covariant version but haven't been able to look into it yet, thanks!

The path that a photon would take from the screen to the orbit that would not fall into the BH, would this correspond to any entropy? Or should I be looking at this description as light emitted from the horizon going towards the screen maps entropy only?

Why anything? With my extremely limited knowledge of what's going on here, it seems like the entropy being mapped to this screen is more of a mathematical concept.

I'm looking at Bekenstein's bound. I've heard of this covariant version but haven't been able to look into it yet, thanks!
It's a mathematical concept that purports to describe something which may be real. If so, we'd need to measure those fluctuations... or find some other means to verify or falsify the notion.

From my understanding, again... limited, you'd want to be examining the Bekenstein Bound, not the CEB. I don't know however, if examining the CEB would give you the information needed to run that experiment...

Anyway, in theory the fluctuations are defined by the points at which light passes the event horizon. If we use nothing, and just math, it's interesting but unhelpful to any future development of the principle.