Two-Dimensional Reduced Theory and General Static Solution for Uncharged Black p-Branes

We derive a two-dimensional effective dilaton - gravity - matter action that describes the dynamics of an uncharged black p-brane in N dimensions. We show that this effective theory is completely integrable in the static sector and establish its general static solution. The solution includes, as a particular case, the boost symmetric p-brane solution investigated in hep-th/9510202 .