Evaporation of black holes in flat space entangled with an auxiliary universe

Abstract

We study a thermofield double type entangled state on two disjoint universes $A$ and $B$, where one of the universes is asymptotically flat containing a black hole. As we increase the entanglement temperature, this black hole receives back-reaction from the stress energy tensor of the state. This results in lengthening of the wormhole region in the black hole interior, and decreasing of its horizon area, both of which are key features of an evaporating black hole. We then compute the entanglement entropy on the universe $A$ through the island formula, and argue that it naturally follows the Page curve of an evaporating black hole in flat space. We also study the effects of local operations in the gravitating universe with the black hole. We find that they accelerate the evaporation of the black hole, therefore disrupt the entanglement between two universes. Furthermore, we observe that depending on whether the operation can be regarded as an LOCC or not, the behavior of the entanglement entropy changes. In particular, when the operation is made neither in the entanglement wedge of the radiation system or that of the black hole, the transition between the island phase and the no-island phase can happen multiple times.

40 pages, 23 figures; v2: minor modifications, typos corrected, references added

References in corpus (5)

• The entropy of Hawking radiation
• Entanglement and correlation functions following a local quench: a conformal field theory approach
• An Information Paradox and Its Resolution in de Sitter Holography
• Entanglement entropy in holographic moving mirror and Page curve
• Islands and stretched horizon

Cited by in corpus (8)

• Page curves for a family of exactly solvable evaporating black holes
• Defect Extremal Surface for Reflected Entropy
• Island for Gravitationally Prepared State and Pseudo Entanglement Wedge
• Entanglement between two gravitating universes
• Entanglement between two evaporating black holes
• A comment on a fine-grained description of evaporating black holes with baby universes
• Page Curve from Defect Extremal Surface and Island in Higher Dimensions
• Holographic moving mirrors