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 \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${{\mathbb R}\times U(1)^{D-3}}$$\end{document}. 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.