Uniqueness theorem for stationary black hole solutions of \sigma-models in five dimensions

TL;DR

This paper proves a uniqueness theorem for five-dimensional stationary black hole solutions in non-linear sigma-models, showing that the Myers-Perry vacuum Kerr spacetime is the only such solution with specific properties.

Contribution

It establishes the first uniqueness theorem for stationary black holes in five-dimensional sigma-models, identifying the Myers-Perry spacetime as the unique solution under given conditions.

Findings

Myers-Perry spacetime is unique under the specified conditions.

The theorem applies to asymptotically flat, stationary, axisymmetric solutions.

Regular rotating event horizon with constant mapping is a key condition.

Abstract

We prove the uniqueness theorem for stationary self-gravitating non-linear \sigma-models in five-dimensional spacetime. We show that the Myers-Perry vacuum Kerr spacetime is the only maximally extended, stationary, axisymmetric, asymptotically flat solution having the regular rotating event horizon with constant mapping.