Uniqueness Theorem for Static Black Hole Solutions of sigma-models in Higher Dimensions

TL;DR

This paper proves that in higher dimensions, the Schwarzschild-Tangherlini spacetime is the unique static, asymptotically flat black hole solution with a regular horizon in non-linear sigma-models, using the positive mass theorem.

Contribution

It establishes a uniqueness theorem for static black holes in higher-dimensional sigma-models, extending classical results to more complex theories.

Findings

Schwarzschild-Tangherlini spacetime is unique under specified conditions.

The positive mass theorem is used to prove the uniqueness.

The result applies to non-rotating, regular horizon solutions in higher dimensions.

Abstract

We prove the uniqueness theorem for self-gravitating non-linear sigma-models in higher dimensional spacetime. Applying the positive mass theorem we show that Schwarzschild-Tagherlini spacetime is the only maximally extended, static asymptotically flat solution with non-rotating regular event horizon with a constant mapping.