Black hole entropy from non-Dirichlet sectors, and bounce solution

TL;DR

This paper investigates black hole entropy through boundary degrees of freedom, critiques Wald's formula, and introduces a generalized entropy concept involving non-Dirichlet boundary conditions and bounce solutions, linking entropy to entanglement.

Contribution

It advances understanding of black hole entropy by focusing on boundary dynamics, addressing limitations of Wald's formula, and incorporating non-Dirichlet conditions and bounce solutions for a unified entropy framework.

Findings

Wald's entropy formula correctly captures black hole entropy under certain conditions

Discrepancies between holographic and Wald's entropies are explained

Black hole entropy is interpreted as entanglement entropy in a thermodynamic context

Abstract

In a series of recent works the relevance of gravitational boundary degrees of freedom and their dynamics in gravity quantization and black hole information has been explored. In this work we further the progress by keenly focusing on the boundary degrees of freedom as the origin of black hole entropy. Wald's entropy formula is scrutinized, and the reason that the Wald's formula correctly captures the entropy of a black hole is examined. Afterwards, limitations of the Wald's method are discussed; a coherent view of entropy based on boundary dynamics is presented. The discrepancy observed in the literature between holographic and Wald's entropies is addressed. We generalize the entropy definition so as to handle a time-dependent black hole. Large gauge symmetry plays a pivotal role. Non-Dirichlet boundary conditions and gravitational analogues of Coleman-De Luccia bounce solutions are central in identifying the microstates and differentiating the origins of entropies associated with different classes of solutions. The result in the present work leads to a view that black hole entropy is entanglement entropy in a thermodynamic setup.