Entropy of 4D Extremal Black Holes

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.