Apparent horizons associated with dynamical black hole entropy
Phys. Rev. D 112, 104049 – Published 18 November, 2025
DOI: https://doi.org/10.1103/f2t6-7t61
Abstract
We define entropic marginally outer trapped surfaces (E-MOTSs), associated with a given entropy density, 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 et al., defined on a background Killing horizon, can be expressed as the Wall entropy evaluated on an E-MOTS associated with it in any diffeomorphism invariant theory of gravity. 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.
