Semi-classical thermodynamics of quantum extremal surfaces in Jackiw-Teitelboim gravity

Abstract

Quantum extremal surfaces (QES), codimension-2 spacelike regions which extremize the generalized entropy of a gravity-matter system, play a key role in the study of the black hole information problem. The thermodynamics of QESs, however, has been largely unexplored, as a proper interpretation requires a detailed understanding of backreaction due to quantum fields. We investigate this problem in semi-classical Jackiw-Teitelboim (JT) gravity, where the spacetime is the eternal two-dimensional Anti-de Sitter (AdS 2 ) black hole, Hawking radiation is described by a conformal field theory with central charge c, and backreaction effects may be analyzed exactly. We show the Wald entropy of the semi-classical JT theory entirely encapsulates the generalized entropy -including time-dependent von Neumann entropy contributions -whose extremization leads to a QES lying just outside of the black hole horizon. Consequently, the QES defines a Rindler wedge nested inside the enveloping black hole. We use covariant phase space techniques on a time-reflection symmetric slice to derive a Smarr relation and first law of nested Rindler wedge thermodynamics, regularized using local counterterms, and including semi-classical effects. Moreover, in the microcanonical ensemble the semi-classical first law implies the generalized entropy of the QES is stationary at fixed energy. Thus, the thermodynamics of the nested Rindler wedge is equivalent to thermodynamics of the QES in the microcanonical ensemble.

Holographic CFT Phase Transitions and Criticality for Charged AdS Black Holes

“…Θ = − 1 d Ω d−1 r d h [16,26]. Instead of using the background subraction method one can also employ the counterterm subtraction method to regulate the divergence in the Killing volume [33].…”

Holographic JT gravity with quartic couplings

“…• In Section (7), we explore thermal properties of 2D black holes in our model. In particular, we discuss the Wald entropy [67]- [69] for 2D black holes and observe that the Wald entropy diverges near the horizon due to the presence of higher derivative interactions. We interpret these divergences in terms of the density of states [70]- [72].…”