Black hole mass formula in the membrane paradigm

TL;DR

This paper derives the black hole mass formula using the membrane paradigm, extending its application to self-gravitating membranes in static and stationary black hole spacetimes with or without electric fields.

Contribution

It provides a direct derivation of the black hole mass formula within the membrane paradigm, including cases with electric fields and self-gravitating membranes.

Findings

Derived the black hole mass formula in static and stationary cases.

Extended the membrane paradigm to self-gravitating membranes.

Applicable to black holes with electric fields.

Abstract

The membrane paradigm approach adopts a timelike surface, stretched out off the null event horizon, to study several important black hole properties. We use this powerful tool to give a direct derivation of the black hole mass formula in the static and stationary cases without and with electric field. Since here the membrane is a self-gravitating material system we go beyond the usual applicability on test particles and test fields of the paradigm.