A uniqueness theorem for stationary Kaluza-Klein black holes

TL;DR

This paper proves a uniqueness theorem for stationary Kaluza-Klein black holes in higher dimensions, showing their topology and metric are uniquely determined by angular momenta and specific invariants.

Contribution

It establishes a new uniqueness result for higher-dimensional Kaluza-Klein black holes with multiple symmetries, detailing how their properties are uniquely specified by invariants.

Findings

Black hole topology and metrics are uniquely determined by angular momenta.

The invariants include real moduli and integer vectors with constraints.

The theorem applies to stationary D-dimensional Kaluza-Klein black holes with specific symmetries.

Abstract

We prove a uniqueness theorem for stationary $D$-dimensional Kaluza-Klein black holes with $D-2$ Killing fields, generating the symmetry group ${\mathbb R} \times U(1)^{D-3}$. It is shown that the topology and metric of such black holes is uniquely determined by the angular momenta and certain other invariants consisting of a number of real moduli, as well as integer vectors subject to certain constraints.