Unified First Law and Thermodynamics of Dynamical Black Hole in n-dimensional Vaidya Spacetime

TL;DR

This paper explores the thermodynamics of dynamical black holes in n-dimensional Vaidya spacetime, deriving the unified first law and discussing the second law, thus extending black hole thermodynamics to dynamical, higher-dimensional contexts.

Contribution

It derives the unified first law and the first law of dynamical black holes in n-dimensional Vaidya spacetime using Hayward's methods, extending thermodynamic understanding to dynamical, higher-dimensional black holes.

Findings

Derived the unified first law for n-dimensional Vaidya spacetime.

Obtained the first law of dynamical black holes by projecting the unified law.

Discussed the second law of dynamical black holes.

Abstract

As a simple but important example of dynamical black hole, we analysis the dynamical black hole in $n$-dimensional Vaidya spacetime in detail. We investigated the thermodynamics of field equation in $n$-dimensional Vaidya spacetime. The unified first law was derived in terms of the methods proposed by Sean A Hayward. The first law of dynamical black hole was obtained by projecting the unified first law along the trapping horizon. At last, the second law of dynamical black hole is also discussed.