Black Hole Entropy from BPS Closed String

TL;DR

This paper calculates the entropy of extremal five-dimensional black holes using BPS closed strings, showing agreement with Bekenstein-Hawking entropy and exploring the connection between different string configurations and open string pictures.

Contribution

It introduces a novel approach using BPS closed strings with and without winding to derive black hole entropy, linking closed and open string descriptions.

Findings

Black hole entropy matches Bekenstein-Hawking entropy.

Two string configurations yield the same entropy.

Proposed equivalence between winding and non-winding closed strings.

Abstract

By using BPS closed string, the entropy is calculated of the extremal five dimensional black hole consisting of Dirichlet onebranes, Dirichlet fivebranes and Kaluza-Klein momentum in the flat background approximation. In our formulations we consider two kinds of BPS closed strings with or without a winding number. In the former case heavy excitation modes of closed strings are used to derive the entropy. In the latter case we have no oscillator modes and consider collective motion of such massless closed strings. The entropy is given by the number of the ways how we divide the Kaluza-Klein momentum among the massless closed strings. In both cases the black hole entropy is the same as the Bekenstein-Hawking entropy. We argue that the collective modes of closed strings without winding is equivalent to a single closed string with winding. We propose that the two closed string pictures are connected with the open string pictures by the modular transformation.