A uniqueness theorem for stationary Kaluza-Klein black holes

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.