On the physical process first law for dynamical black holes

TL;DR

This paper investigates the mathematical structure of the physical process first law of black hole mechanics in general diffeomorphism invariant theories, analyzing entropy ambiguities and extending the law to non-stationary horizons.

Contribution

It provides a detailed analysis of the physical process first law's structure, clarifies the impact of entropy ambiguities, and extends the law to non-stationary horizons in general gravity theories.

Findings

Integrated entropy change is ambiguity-independent for linearized perturbations.

Additional contributions to entropy change relate to horizon fluid energy.

Extended the first law to non-stationary horizons in general relativity and Lanczos-Lovelock gravity.

Abstract

Physical process version of the first law of black hole mechanics relates the change in entropy of a perturbed Killing horizon, between two asymptotic cross sections, to the matter flow into the horizon. Here, we study the mathematical structure of the physical process first law for a general diffeomorphism invariant theory of gravity. We analyze the effect of ambiguities in the Wald's definition of entropy on the physical process first law. We show that for linearized perturbations, the integrated version of the physical process law, which determines the change of entropy between two asymptotic cross-sections, is independent of these ambiguities. In case of entropy change between two intermediate cross sections of the horizon, we show that it inherits additional contributions, which coincide with the membrane energy associated with the horizon fluid. Using this interpretation, we write down a physical process first law for entropy change between two arbitrary non-stationary cross sections of the horizon for both general relativity and Lanczos-Lovelock gravity.