A boundary value problem for the five-dimensional stationary rotating black holes

TL;DR

This paper proves the uniqueness of five-dimensional stationary rotating black holes with specific symmetries, showing they are fully characterized by mass and angular momenta.

Contribution

It establishes a uniqueness theorem for five-dimensional rotating black holes under certain symmetry and topology assumptions.

Findings

Black holes are uniquely determined by mass and angular momenta.

The proof relies on boundary value problem analysis for Einstein's equations.

Assumes two rotational symmetries and spherical horizon topology.

Abstract

We study the boundary value problem for the stationary rotating black hole solutions to the five-dimensional vacuum Einstein equation. Assuming the two commuting rotational symmetry and the sphericity of the horizon topology, we show that the black hole is uniquely characterized by the mass, and a pair of the angular momenta.