Dynamical surface gravity

TL;DR

This paper explores various classical definitions of surface gravity for dynamical black holes, comparing different proposals in spherically symmetric spacetimes and relating trapping horizon formalism to other approaches.

Contribution

It systematically compares multiple definitions of surface gravity for dynamical black holes and clarifies their relationships in spherically symmetric cases.

Findings

Different definitions yield distinct surface gravity values.

The trapping horizon formalism can be connected to other surface gravity constructions.

The paper clarifies the applicability of various proposals to dynamical horizons.

Abstract

We discuss how the surface gravity can be classically defined for dynamical black holes. In particular we focus on defining the surface gravity for locally defined horizons and compare a number definitions proposed in the literature. We illustrate the differences between the various proposals in the case of an arbitrary dynamical, spherically symmetric black hole spacetime. We also discuss how the trapping horizon formalism of Hayward can be related to other constructions.