Statistical Entropy of Schwarzschild Black Strings and Black Holes

TL;DR

This paper calculates the statistical entropy of five-dimensional Schwarzschild black strings using conformal symmetry, matching it with the classical Bekenstein-Hawking entropy for both black strings and four-dimensional black holes.

Contribution

It introduces a method to derive the black string's entropy via near-horizon conformal symmetry, aligning quantum state counting with classical entropy results.

Findings

Statistical entropy matches Bekenstein-Hawking entropy for black strings and black holes.

The conformal symmetry approach reproduces the precise entropy value.

The string length choice aligns with the Virasoro algebra and stability bounds.

Abstract

The statistical entropy of a Schwarzschild black string in five dimensions is obtained by counting the black string states which form a representation of the near-horizon conformal symmetry with a central charge. The statistical entropy of the string agrees with its Bekenstein-Hawking entropy as well as that of the Schwarzschild black hole in four dimensions. The choice of the string length which gives the Virasoro algebra also reproduces the precise value of the Bekenstein-Hawking entropy and lies inside the stability bound of the string.