On the Wikipedia page for the Black Hole Information paradox, it states that

More precisely, if there is an entangled pure state, and one part of the entangled system is thrown into the black hole while keeping the other part outside, the result is a mixed state after the partial trace is taken into the interior of the black hole. But since everything within the interior of the black hole will hit the singularity within a finite time, the part which is traced over partially might disappear completely from the physical system.

No citation is given, and I have been trying to find another resource that gives me a similar description of the loss of information in a black hole, but I've found nothing. If someone could give me a solid reference for this idea (which could be understood by someone with a Thorne, Misner & Wheeler level of understanding of GR), it would be greatly appreciated. If the Penrose diagram on that same page described an eternal black hole (i.e., no Hawking radiation), would information still be lost?


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Actually the explanation is a bit misleading. What is true is that (in conventional General Relativity + Quantum Field Theory in curved space) the Hawking radiation is completely thermal. If we consider the bipartite system black hole-radiation and we trace out over the black hole, the resulting system is maximally mixed (the density matrix is diagonal, that is every state is equally likely, therefore there is no way to retrieve information of what entered the black hole.)

Since the density matrix of the traced system is maximally mixed, the black hole and the radiation are by definition maximally entangled. If the black hole is stable there is no problem, since the whole system black hole + radiation can be still considered pure, even though the information is forever stored inside the horizon. The paradox arises when the black hole evaporates completely. At this point what is left is thermal radiation without information, and apparently without an entangled partner.

It is explained in some detail in:



Harlow (2015)

(in the first two references, the focus is on entangled pairs created on the horizon, but the reasoning is the same)


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