Mass and Thermodynamics of Kaluza-Klein Black Holes with Squashed Horizons

TL;DR

This paper calculates the mass and explores the thermodynamics of a five-dimensional Kaluza-Klein black hole with a squashed horizon, comparing it to known black hole solutions and confirming thermodynamic laws.

Contribution

It applies boundary counterterm and generalized Abbott-Deser methods to compute the mass of the black hole, confirming the first law of thermodynamics for this specific spacetime.

Findings

Mass calculated consistently by two methods.

Thermodynamic properties discussed and compared.

First law of black hole thermodynamics verified.

Abstract

Recently a five-dimensional Kaluza-Klein black hole solution with squashed horizon has been found in hep-th/0510094. The black hole spacetime is asymptotically locally flat and has a spatial infinity $S^1 \hookrightarrow S^{2}$. 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-Nordstr\"om black hole.