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 time-like Killing vector 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, we explicitly give the solutions in 11-dimensional M theory for the case with M2⊥ M2⊥ M2 intersecting branes. Compactifying these solutions into five dimensions, we show that these solutions include the supersymmetric black ring solution. We prove that the solutions preserve the 1/8 supersymmetry if the gravi-electromagnetic field , which is a rotational part of gravity, is self-dual, or to add the additional constraint for the integral constants.