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.

Latex, 38 pages, no figures; v2: removed condition from statement of main theorem, additional material on spacetime topology, references added