Semiclassical thermodynamics of quantum extremal surfaces in JackiwTeitelboim gravity
Abstract
Quantum extremal surfaces (QES), codimension2 spacelike regions which extremize the generalized entropy of a gravitymatter 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 semiclassical JackiwTeitelboim (JT) gravity, where the spacetime is the eternal twodimensional Antide 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 semiclassical JT theory entirely encapsulates the generalized entropy — including timedependent 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 timereflection symmetric slice to derive a Smarr relation and first law of nested Rindler wedge thermodynamics, regularized using local counterterms, and intrinsically including semiclassical effects. Moreover, in the microcanonical ensemble the semiclassical 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 the thermodynamics of the QES in the microcanonical ensemble.
 Publication:

Journal of High Energy Physics
 Pub Date:
 December 2021
 DOI:
 10.1007/JHEP12(2021)134
 arXiv:
 arXiv:2107.10358
 Bibcode:
 2021JHEP...12..134P
 Keywords:

 2D Gravity;
 Black Holes;
 AdSCFT Correspondence;
 High Energy Physics  Theory;
 General Relativity and Quantum Cosmology
 EPrint:
 101 pages, 5 appendices, 3 figures