Entropy of 4D Extremal Black Holes

TL;DR

This paper derives the Bekenstein-Hawking entropy for 4D extremal black holes using two T-dual weak coupling string theory models involving D-branes, confirming the entropy formula in different duality frames.

Contribution

It provides a novel derivation of black hole entropy in string theory through two distinct T-dual weak coupling approaches involving D-brane bound states.

Findings

Entropy matches Bekenstein-Hawking formula in both models

Demonstrates consistency of dual descriptions of extremal black holes

Validates string theory methods for black hole entropy calculation

Abstract

We derive the Bekenstein-Hawking entropy formula for four-dimensional Reissner-Nordstrom extremal black holes in type II string theory. The derivation is performed in two separate (T-dual) weak coupling pictures. One uses a type IIB bound state problem of D5- and D1-branes, while the other uses a bound state problem of D0- and D4-branes with macroscopic fundamental type IIA strings. In both cases, the D-brane systems are also bound to a Kaluza-Klein monopole, which then yields the four-dimensional black hole at strong coupling.