Conformal Killing horizons and their thermodynamics

TL;DR

This paper explores how conformal transformations relate dynamical black hole horizons to static ones, enabling the derivation of thermodynamic properties for dynamical black holes using conformal Killing horizons.

Contribution

It introduces a method to derive thermodynamics of dynamical black holes via conformal Killing horizons, linking them to static spacetime horizons.

Findings

Conformal Killing horizons can be used to analyze dynamical black hole thermodynamics.

The approach applies to Vaidya spacetime with null dust accretion.

Conformal relation provides a local, physically meaningful horizon concept.

Abstract

Certain dynamical black hole solutions can be mapped to static spacetimes by conformal metric transformations. This mapping provides a physical link between the conformal Killing horizon of the dynamical black hole and a Killing horizon of the static spacetime. We show how this conformal relation can be used to derive thermodynamic properties for the dynamical black holes. Although these horizons are defined quasi-locally and can be located by local experiments, they are distinct from other popular notions of quasi-local horizons such as apparent horizons. Thus in the dynamical Vaidya spacetime describing constant accretion of null dust, the conformal Killing horizon, which is null by construction, is the natural horizon to describe the black hole.