Statistical Entropy of Schwarzschild Black Holes

TL;DR

This paper calculates the entropy of seven-dimensional Schwarzschild black holes by mapping them onto near extremal self-dual three-branes, providing a string theory-based derivation of their entropy consistent with Bekenstein-Hawking formula.

Contribution

It introduces a novel method to derive black hole entropy using duality and brane mappings, extending to lower-dimensional black holes.

Findings

Entropy matches Bekenstein-Hawking value up to a factor of one

Method applies to five and four dimensional black holes

Partition function of three-brane evaluated explicitly

Abstract

The entropy of a seven dimensional Schwarzschild black hole of arbitrary large radius is obtained by a mapping onto a near extremal self-dual three-brane whose partition function can be evaluated. The three-brane arises from duality after submitting a neutral blackbrane, from which the Schwarzschild black hole can be obtained by compactification, to an infinite boost in non compact eleven dimensional space-time and then to a Kaluza-Klein compactification. This limit can be defined in precise terms and yields the Bekenstein-Hawking value up to a factor of order one which can be set to be exactly one with the extra assumption of keeping only transverse brane excitations. The method can be generalized to five and four dimensional black holes.