Remarks on the Entropy of Non-Stationary Black Holes

TL;DR

This paper extends the concept of black hole entropy from stationary to non-stationary cases, defining it as a thermodynamic quantity satisfying the first law, with additional volume terms due to the lack of a Killing vector.

Contribution

It introduces a generalized entropy definition applicable to non-stationary black holes, incorporating volume terms absent in stationary cases.

Findings

Entropy satisfies the first law of thermodynamics.

Volume terms appear in the entropy expression for non-stationary black holes.

Extension of entropy concept beyond stationary solutions.

Abstract

The definition of entropy obtained for stationary black holes is extended in this paper to the case of non-stationary black holes. Entropy is defined as a macroscopical thermodynamical quantity which satisfies the first principle of thermodynamics. In the non-stationary case a volume term appears since the solution does not admit a Killing vector.