A revision to the QES prescription

TL;DR

This paper revises the Quantum Extremal Surface (QES) prescription for black hole entanglement entropy, addressing limitations of the original derivation and proposing a more comprehensive formula that aligns with unitarity and the Page curve.

Contribution

It introduces a refined QES formula involving multiple surfaces, improving the theoretical understanding of black hole entropy calculations.

Findings

Consistent with early and late black hole evaporation stages.

Aligns with the unitary Page curve.

Addresses challenges in the replica trick derivation.

Abstract

In this paper, we propose a revision to the Quantum Extremal Surface (QES) prescription, which plays a crucial role in describing the entanglement entropy of black holes. While derivations exist for the original QES prescription using the replica trick, they rely on a saddle point approximation that faces challenges when the number of replicas approaches unity. We highlight these challenges and derive a refined formula for the entanglement entropy that incorporates a weighted summation over multiple surfaces, contrasting the QES prescription's reliance on a single extremal surface. We validate our formulation by demonstrating consistency with expected results for both the early and late stages of black hole evaporation, confirming its alignment with the unitary evolution depicted by the Page curve.