Membrane paradigm and entropy of black holes in the Euclidean action approach

TL;DR

This paper combines the membrane paradigm and Euclidean action approaches to derive black hole entropy, providing insights into black hole properties without electric fields.

Contribution

It introduces a method that integrates membrane paradigm and Euclidean action techniques to directly derive black hole entropy.

Findings

Derived black hole entropy using combined approaches

Clarified the role of the stretched horizon in entropy calculation

Provided a framework for analyzing black hole properties without electric fields

Abstract

The membrane paradigm approach to black holes fixes in the vicinity of the event horizon a fictitious surface, the stretched horizon, so that the spacetime outside remains unchanged and the spacetime inside is vacuum. Using this powerful method, several black hole properties have been found and settled, such as the horizon's viscosity, electrical conductivity, resistivity, as well as other properties. On the other hand the Euclidean action approach to black hole spacetimes has been very fruitful in understanding black hole entropy. Combining both the Euclidean action and membrane paradigm approaches a direct derivation of the black hole entropy is given. In the derivation it is considered that the only fields present are the gravitational and matter fields, with no electric field.