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How does the Holographic Principle help to establish the fact that all the information is not lost in a black hole?

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because then the information is not lost, its just present in the event horizon. – Vineet Menon Apr 3 '12 at 11:23
@Vineet that could be an answer – David Z Apr 3 '12 at 23:54
Related: – Qmechanic Apr 4 '12 at 6:48

As I said in the comment, the information is not lost simply because of the holographic image at event horizon. This was the result of a long 20 year battle between Susskind and Hawking. Susskind had the final laugh!

I suggest you to read the wiki pages: Black hole information paradox,Holographic Principle

I'll quote an excerpt from wiki,

This idea was made more precise by Leonard Susskind, who had also been developing holography, largely independently. Susskind argued that the oscillation of the horizon of a black hole is a complete description of both the infalling and outgoing matter, because the world-sheet theory of string theory was just such a holographic description. While short strings have zero entropy, he could identify long highly excited string states with ordinary black holes. This was a deep advance because it revealed that strings have a classical interpretation in terms of black holes.

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The Holographic principle is one manifestation of the ADS/CFT correspondence - it's mentioned in the Wikipedia article you cited. The correspondence means that the same black hole can be described using a 5D string theory and a 4D (supersymmetric) field theory. The two are just different ways of describing the same object. In the 5D string theory black holes look quite simple and it's obvious there is no information loss, so we can be confident that there is no information loss in the 4D description either.

So far so good, but no-one knows how to describe the information "no loss"in 4D. Susskind's proposal is possible, but I'm sure he would agree it's not a proof. If someone could work out exactly how the "no loss" in 5D is described in 4D that would be quit a step forward.

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It's the other way around--- the AdS/CFT correspondence is one manifestation of the holographic principle, relevant for physics very close to extremally charge black holes, in particular string branes of various sorts. The general principle is just a way of making unitarity work out in black holes in general, including ordinary uncharged black holes, which have no AdS region. You can deduce that ordinary black hole evaporation is unitary from AdS/CFT, but it doesn't give you the holographic map for ordinary black holes, which is not worked out in any quantitative way yet. – Ron Maimon Jul 5 '12 at 6:57

I would expect the resolution of this dilemma to hold no relation whatsoever to AdS/CFT, being it specific to anti de Sitter spaces, which makes it irrelevant to our universe (unless someone proves an analog version for de Sitter spaces, which seems unlikely)

see this answer for details about an alternative resolution.

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The AdS/CFT is relevant because you can make the AdS radius enormous and approximate flat spacetime. It is ridiculous to assume that black hole evaporation is unitary in nearly flat AdS, but not unitary in our space, especially when the hole is small compared to cosmological sizes in both cases. What is possible is that the cosmological horizon is not like a black hole horizon, in that it is a true mixed state. We can't rule that out because by definition, we only see one cosmological horizon, and any experiment to see that it is in a pure state seems impossible to formulate from inside. – Ron Maimon Jul 5 '12 at 7:00

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