Mass and thermodynamics of Kaluza-Klein black holes with squashed horizons

Recently a five-dimensional Kaluza-Klein black hole solution with squashed horizon has been found in [H. Ishihara, K. Matsuno, hep-th/0510094]. The black hole space-time is asymptotically locally flat and has a spatial infinity S1↪S2. By using “boundary counterterm” method and generalized Abbott-Deser method, we calculate the mass of this black hole. When an appropriate background is chosen, the generalized Abbott-Deser method gives the same mass as the “boundary counterterm” method. The mass is found to satisfy the first law of black hole thermodynamics. The thermodynamic properties of the Kaluza-Klein black hole are discussed and are compared to those of its undeformed counterpart, a five-dimensional Reissner-Nordström black hole.