Microcanonical action and the entropy of Hawking radiation

Juan F. Pedraza; Andrew Svesko; Watse Sybesma; Manus R. Visser

doi:10.1103/PhysRevD.105.126010

Microcanonical action and the entropy of Hawking radiation

Juan F. Pedraza
, Andrew Svesko
, Watse Sybesma
, Manus R. Visser

Science Institute

University of Iceland

Research output: Contribution to journal › Article › peer-review

Abstract

The island formula - an extremization prescription for generalized entropy - is known to result in a unitary Page curve for the entropy of Hawking radiation. This semiclassical entropy formula has been derived for Jackiw-Teitelboim (JT) gravity coupled to conformal matter using the "replica trick"to evaluate the Euclidean path integral. Alternatively, for eternal Anti-de Sitter black holes, we derive the extremization of generalized entropy from minimizing the microcanonical action of an entanglement wedge. The on-shell action is minus the entropy and arises in the saddle-point approximation of the (nonreplicated) microcanonical path integral. When the black hole is coupled to a bath, islands emerge from maximizing the entropy at fixed energy, consistent with the island formula. Our method applies to JT gravity as well as other two-dimensional dilaton gravity theories.

Original language	English
Article number	126010
Journal	Physical Review D
Volume	105
Issue number	12
DOIs	https://doi.org/10.1103/PhysRevD.105.126010
Publication status	Published - 6 Jun 2022

Bibliographical note

Funding Information: We are grateful to B. Banihashemi, T. Banks, P. Draper, R. Emparan, A. Frassino, F. Gautason, T. Jacobson, D. Marolf, J. Sonner, M. Tomasevic, E. Verlinde and A. Wall for useful discussions. A. S. and M. V. acknowledge the University of Barcelona for hospitality while this work was being completed. J. P. is supported by “la Caixa” Foundation (ID 100010434), fellowship code LCF/BQ/PI21/11830029, and by the European Union’s Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie Grant agreement No. 847648. A. S. is supported by the Simons Foundation through It from Qubit: Simons Collaboration on Quantum Fields, Gravity, and Information. W. S. is supported by the Icelandic Research Fund (IRF) via a Personal Postdoctoral Fellowship Grant (185371-051). M. V. is supported by the Swiss National Science Foundation, through Project Grants No. 200020-182513 and No. 51NF40-141869 The Mathematics of Physics (SwissMAP). Publisher Copyright: © 2022 authors. Published by the American Physical Society.

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abstract = "The island formula - an extremization prescription for generalized entropy - is known to result in a unitary Page curve for the entropy of Hawking radiation. This semiclassical entropy formula has been derived for Jackiw-Teitelboim (JT) gravity coupled to conformal matter using the {"}replica trick{"}to evaluate the Euclidean path integral. Alternatively, for eternal Anti-de Sitter black holes, we derive the extremization of generalized entropy from minimizing the microcanonical action of an entanglement wedge. The on-shell action is minus the entropy and arises in the saddle-point approximation of the (nonreplicated) microcanonical path integral. When the black hole is coupled to a bath, islands emerge from maximizing the entropy at fixed energy, consistent with the island formula. Our method applies to JT gravity as well as other two-dimensional dilaton gravity theories.",

author = "Pedraza, \{Juan F.\} and Andrew Svesko and Watse Sybesma and Visser, \{Manus R.\}",

note = "Funding Information: We are grateful to B. Banihashemi, T. Banks, P. Draper, R. Emparan, A. Frassino, F. Gautason, T. Jacobson, D. Marolf, J. Sonner, M. Tomasevic, E. Verlinde and A. Wall for useful discussions. A. S. and M. V. acknowledge the University of Barcelona for hospitality while this work was being completed. J. P. is supported by “la Caixa” Foundation (ID 100010434), fellowship code LCF/BQ/PI21/11830029, and by the European Union{\textquoteright}s Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie Grant agreement No. 847648. A. S. is supported by the Simons Foundation through It from Qubit: Simons Collaboration on Quantum Fields, Gravity, and Information. W. S. is supported by the Icelandic Research Fund (IRF) via a Personal Postdoctoral Fellowship Grant (185371-051). M. V. is supported by the Swiss National Science Foundation, through Project Grants No. 200020-182513 and No. 51NF40-141869 The Mathematics of Physics (SwissMAP). Publisher Copyright: {\textcopyright} 2022 authors. Published by the American Physical Society.",

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Microcanonical action and the entropy of Hawking radiation

Abstract

Bibliographical note

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