Stationary spacetime from intersecting M-branes

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). General solutions are constructed by superposition of a complete set of those harmonic functions. Using the hyperspherical coordinate system for a conformally flat base space, we explicitly give the solutions in 11-dimensional M theory for the case with M2⊥M5 intersecting branes and a traveling wave. Compactifying these solutions into five dimensions, we show that these solutions include the BMPV black hole and the Brinkmann wave solution, and those extension to non-BPS ones. We also find new solutions similar to the Brinkmann wave. We prove that the solutions preserve the 1/8 supersymmetry if the gravi-electromagnetic field Fij, which is a rotational part of gravity, is self-dual. We also discuss non-spherical “black” objects (e.g., a ring topology and an elliptical shape) by use of other curvilinear coordinates.