Thermodynamics of five-dimensional static three-charge STU black holes with squashed horizons

Abstract

We present a new expression for the five-dimensional static Kaluza-Klein black hole solution with squashed $S^3$ horizons and three different charge parameters. This black hole solution belongs to $D=5$ $N=2$ supergravity theory, its spacetime is locally asymptotically flat and has a spatial infinity $R\times S^1\hookrightarrow S^2$. The form of the solution is extraordinary simple and permits us very conveniently to calculate its conserved charges by using the counterterm method. It is further shown that our thermodynamical quantities perfectly obey both the differential and the integral first laws of black hole thermodynamics if the length of the compact extra-dimension can be viewed as a thermodynamical variable.

10 pages, no figure

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• Thermodynamics and topological classifications of static non-extremal four-charge AdS black hole in the five-dimensional $\mathcal{N}=2$, $STU-W^{2}U$ gauged supergravity
• Stationary scalar hairy configurations supported by Neumann compact stars
• New forms and thermodynamics of the neutral rotating squashed black hole in five-dimensional vacuum Einstein gravity theory
• Four-charge static non-extremal black holes in the five-dimensional $\mathcal{N}=2$, $STU-W^{2}U$ supergravity
• Static four-charge squashed black hole in five-dimensional $STU-W^{2}U$ supergravity and its thermodynamics