New Axisymmetric Stationary Solutions of Five-dimensional Vacuum Einstein Equations with Asymptotic Flatness

Abstract

New axisymmetric stationary solutions of the five‐dimensional vacuum Einstein equations are obtained by using solitonic solution‐generating techniques. The solution‐generation is done by reducing the problem to some four‐dimensional one. As a simple and non‐trivial seed, the Weyl‐canocal form of five‐dimensional Minkowski spacetimes is used. The series of new solutions includes one‐rotational black ring solutions which represent the black ring rotating in the azimuthal direction of the two‐dimensional sphere (S2‐rotating black ring). This black ring is different from the one obtained by Emparan and Reall (S1‐rotating black ring).