TY - JOUR

T1 - The fall of the black hole firewall

T2 - Natural nonmaximal entanglement for the Page curve

AU - Hotta, Masahiro

AU - Sugita, Ayumu

N1 - Publisher Copyright:
© 2015 The Author(s).
Copyright:
Copyright 2016 Elsevier B.V., All rights reserved.

PY - 2015/12

Y1 - 2015/12

N2 - The black hole firewall conjecture is based on the Page curve hypothesis, which claims that entanglement between a black hole and its Hawking radiation is almost maximum. Adopting canonical typicality for nondegenerate systems with nonvanishing Hamiltonians, we show the entanglement becomes nonmaximal, and energetic singularities (firewalls) do not emerge for general systems. An evaporating old black hole must evolve in Gibbs states with exponentially small error probability after the Page time as long as the states are typical. This means that the ordinarily used microcanonical states are far from typical. The heat capacity computed from the Gibbs states should be nonnegative in general. However, the black hole heat capacity is actually negative due to the gravitational instability. Consequently the states are not typical until the last burst. This requires inevitable modification of the Page curve, which is based on the typicality argument. For static thermal pure states of a large AdS black hole and its Hawking radiation, the entanglement entropy equals the thermal entropy of the smaller system.

AB - The black hole firewall conjecture is based on the Page curve hypothesis, which claims that entanglement between a black hole and its Hawking radiation is almost maximum. Adopting canonical typicality for nondegenerate systems with nonvanishing Hamiltonians, we show the entanglement becomes nonmaximal, and energetic singularities (firewalls) do not emerge for general systems. An evaporating old black hole must evolve in Gibbs states with exponentially small error probability after the Page time as long as the states are typical. This means that the ordinarily used microcanonical states are far from typical. The heat capacity computed from the Gibbs states should be nonnegative in general. However, the black hole heat capacity is actually negative due to the gravitational instability. Consequently the states are not typical until the last burst. This requires inevitable modification of the Page curve, which is based on the typicality argument. For static thermal pure states of a large AdS black hole and its Hawking radiation, the entanglement entropy equals the thermal entropy of the smaller system.

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U2 - 10.1093/ptep/ptv170

DO - 10.1093/ptep/ptv170

M3 - Article

AN - SCOPUS:84997194350

VL - 2015

JO - Progress of Theoretical and Experimental Physics

JF - Progress of Theoretical and Experimental Physics

SN - 2050-3911

IS - 12

M1 - 123B04

ER -