### 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 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.

Original language | English |
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Article number | S56 |

Pages (from-to) | 7025-7030 |

Number of pages | 6 |

Journal | Journal of Physics A: Mathematical and Theoretical |

Volume | 40 |

Issue number | 25 |

DOIs | |

Publication status | Published - 2007 Jun 22 |

### ASJC Scopus subject areas

- Statistical and Nonlinear Physics
- Statistics and Probability
- Modelling and Simulation
- Mathematical Physics
- Physics and Astronomy(all)

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## Cite this

*Journal of Physics A: Mathematical and Theoretical*,

*40*(25), 7025-7030. [S56]. https://doi.org/10.1088/1751-8113/40/25/S56