Stationary spacetime with intersecting branes in M/superstring theory

We study a stationary "black" brane in M/superstring theory. Assuming BPS-type relations between the first-order derivatives of metric functions, we present general stationary black brane solutions with a traveling wave for the Einstein equations in D-dimensions. The solutions are given by a few independent harmonic equations (and plus the Poisson equation). Using the hyperspherical coordinate system for a flat base space, we explicitly give the solutions in 11-dimensional M theory for the case with M2⊥LM5 intersecting branes and a traveling wave. Compactifying these solutions into five dimensions, we present general solutions, which include the BMPV black hole and the Brinkmann wave solution. We prove that the solutions preserve the 1/8 supersymmetry if the gravi-electromagnetic field F_ij, which is a rotational part of gravity, is self-dual. We also construct a supersymmetric rotating black hole in a compactified 4-dimensional spacetime by superposing an infinite number of BMPV black holes.