Microcanonical Action and the Entropy of Hawking Radiation
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 semi-classical 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.
Keywords
Cite
@article{arxiv.2111.06912,
title = {Microcanonical Action and the Entropy of Hawking Radiation},
author = {Juan F. Pedraza and Andrew Svesko and Watse Sybesma and Manus R. Visser},
journal= {arXiv preprint arXiv:2111.06912},
year = {2022}
}
Comments
5 pages and appendices, 2 figures; minor clarifications added, PRD version