A Note on Intersecting $D$-branes and Black Hole Entropy

TL;DR

This paper explores how four-dimensional extremal black holes with different scalar couplings can be understood as intersections of higher-dimensional non-singular D-brane configurations, leading to a consistent definition of their entropy.

Contribution

It demonstrates that these black holes decompactify into higher-dimensional non-singular solutions, allowing a unified entropy description from a higher-dimensional perspective.

Findings

Black holes decompactify into higher-dimensional non-singular solutions

A consistent entropy can be defined for all four black hole types

Higher-dimensional description clarifies the nature of extremal black holes

Abstract

In four dimensions there are 4 different types of extremal Maxwell/scalar black holes characterized by a scalar coupling parameter $a$ with $a=0,1/\sqrt{3} , 1 , \sqrt{3}$. These black holes can be described as intersections of ten--dimensional non-singular Ramond-Ramond objects, i.e.~$D$-branes, waves and Taub-NUT solitons. Using this description it can be shown that the four--dimensional black holes decompactify near the core to higher--dimensional {\em non-singular} solutions. In terms of these higher--dimensional non-singular solutions we define a non-vanishing entropy for all four black hole types from a four--dimensional point of view.