Uniqueness theorem for stationary black ring solution of $\sigma$-models in five dimensions

TL;DR

This paper proves that in five-dimensional spacetime, the only asymptotically flat black ring solution with a regular horizon in a specific non-linear sigma model is uniquely characterized by mass and angular momenta.

Contribution

It establishes a uniqueness theorem for stationary black ring solutions in five-dimensional sigma models, showing the solution's parameters are uniquely determined.

Findings

Black ring solution is unique under given conditions.

Solution characterized solely by mass and two angular momenta.

No other asymptotically flat black ring solutions with regular horizons exist in this model.

Abstract

We study axisymmetric self-gravitating non-linear $\sigma$-model in five-dimensional spacetime admitting three commutating Killing vector fields. We show that the only asymptotically flat black ring solution with a regular event horizon is the black ring characterized by mass and two angular momenta with constant mapping.