Intersecting D-branes and black hole entropy

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/√3, 1, √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 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