Cool horizons for entangled black holes

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Abstract

General relativity contains solutions in which two distant black holes are connected through the interior via a wormhole, or Einstein-Rosen bridge. These solutions can be interpreted as maximally entangled states of two black holes that form a complex EPR pair. We suggest that similar bridges might be present for more general entangled states. In the case of entangled black holes one can formulate versions of the AMPS(S) paradoxes and resolve them. This suggests possible resolutions of the firewall paradoxes for more general situations.

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Average Entropy of a Subsystem

(2010)

If a quantum system of Hilbert space dimension \(mn\) is in a random pure state, the average entropy of a subsystem of dimension \(m\leq n\) is conjectured to be \(S_{m,n}=\sum_{k=n+1}^{mn}\frac{1}{k}-\frac{m-1}{2n}\) and is shown to be \(\simeq \ln m - \frac{m}{2n}\) for \(1\ll m\leq n\). Thus there is less than one-half unit of information, on average, in the smaller subsystem of a total system in a random pure state.

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The information paradox: A pedagogical introduction

Samir D. Mathur (2009)

The black hole information paradox is a very poorly understood problem. It is often believed that Hawking's argument is not precisely formulated, and a more careful accounting of naturally occurring quantum corrections will allow the radiation process to become unitary. We show that such is not the case, by proving that small corrections to the leading order Hawking computation cannot remove the entanglement between the radiation and the hole. We formulate Hawking's argument as a `theorem': assuming `traditional' physics at the horizon and usual assumptions of locality we will be forced into mixed states or remnants. We also argue that one cannot explain away the problem by invoking AdS/CFT duality. We conclude with recent results on the quantum physics of black holes which show the the interior of black holes have a `fuzzball' structure. This nontrivial structure of microstates resolves the information paradox, and gives a qualitative picture of how classical intuition can break down in black hole physics.

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Information in Black Hole Radiation

Don N. Page (1993)

If black hole formation and evaporation can be described by an \(S\) matrix, information would be expected to come out in black hole radiation. An estimate shows that it may come out initially so slowly, or else be so spread out, that it would never show up in an analysis perturbative in \(M_{Planck}/M\), or in 1/N for two-dimensional dilatonic black holes with a large number \(N\) of minimally coupled scalar fields.