Thermodynamics of Black Hole in (N+3)-dimensions from Euclidean N-brane Theory

TL;DR

This paper explores the thermodynamics of higher-dimensional black holes using an N-brane approach, deriving temperature and entropy formulas, and discussing quantum corrections within a string theory framework.

Contribution

It introduces an N-brane based formalism to analyze (N+3)-dimensional black holes, extending previous four-dimensional models and calculating thermodynamic properties.

Findings

Exact Hawking temperature derived from world line instanton solutions.

Leading order Bekenstein-Hawking entropy formula obtained.

Discussion of one-loop quantum corrections to black hole entropy.

Abstract

In this article we consider an N-brane description of an (N+3)-dimensional black hole horizon. First of all, we start by reviewing a previous work where a string theory is used as describing the dynamics of the event horizon of a four dimensional black hole. Then we consider a particle model defined on one dimensional Euclidean line in a three dimensional black hole as a target spacetime metric. By solving the field equations we find a ``world line instanton'' which connects the past event horizon with the future one. This solution gives us the exact value of the Hawking temperature and to leading order the Bekenstein-Hawking formula of black hole entropy. We also show that this formalism is extensible to an arbitrary spacetime dimension. Finally we make a comment of one-loop quantum correction to the black hole entropy .