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

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.