A rotating Kaluza–Klein black hole with squashed horizons

We find a rotating Kaluza–Klein black hole solution with squashed S3S3 horizons in five dimensions. This is a Kerr counterpart of the charged one found by Ishihara and Matsuno [H. Ishihara, K. Matsuno, Kaluza–Klein black holes with squashed horizons, hep-th/0510094] recently. The space–time is geodesic complete and free of naked singularities. Its asymptotic structure is a twisted S1S1 fiber bundle over a four-dimensional Minkowski space–time. We also study the mass and thermodynamics of this black hole.