Stationary Spacetime from Intersecting M-branes

TL;DR

This paper derives general stationary black brane solutions in M-theory with intersecting branes and traveling waves, revealing new supersymmetric solutions and connections to known black hole and wave solutions.

Contribution

It introduces a unified method to construct stationary black brane solutions with harmonic functions, including new solutions and supersymmetry conditions in M-theory.

Findings

Explicit solutions for intersecting M2-M5 branes with waves in 11D.

Identification of conditions for 1/8 supersymmetry preservation.

Connection of solutions to BMPV black hole and Brinkmann wave.

Abstract

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, 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. 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 F, 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.