Apparent Horizons Associated with Dynamical Black Hole Entropy

TL;DR

This paper introduces entropic marginally outer trapped surfaces (E-MOTSs) as a generalization of apparent horizons and demonstrates that the dynamical black hole entropy can be expressed on these surfaces, ensuring consistency with stationary cases.

Contribution

It defines E-MOTSs and shows that dynamical black hole entropy can be evaluated on them, linking it to Wall entropy and confirming its reduction to Wald entropy in stationary limits.

Findings

Dynamical black hole entropy can be expressed on E-MOTSs.

The formulation reduces to Wald entropy in stationary regimes.

Reinforces robustness of dynamical entropy in black hole physics.

Abstract

We define entropic marginally outer trapped surfaces (E-MOTSs) as a generalization of apparent horizons. We then show that, under first-order perturbations around a stationary black hole, the dynamical black hole entropy proposed by Hollands, Wald, and Zhang, defined on a background Killing horizon, can be expressed as the Wall entropy evaluated on an E-MOTS associated with it. Our result ensures that the Hollands-Wald-Zhang entropy reduces to the standard Wald entropy in each stationary regime of a dynamical black hole, thereby reinforcing the robustness of the dynamical entropy formulation.