A Uniqueness Theorem for Stationary Kaluza-Klein Black Holes

We prove a uniqueness theorem for stationary D-dimensional Kaluza-Klein black holes with D − 2 Killing fields, generating the symmetry group _boxclose_boxclose_boxclose U(1)^D-3{{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.