Wald entropy in Kaluza-Klein black holes

Author:

Gómez-Fayrén CarmenORCID,Meessen PatrickORCID,Ortín TomásORCID,Zatti Matteo

Abstract

Abstract We study the thermodynamics of the 4-dimensional electrically charged black-hole solutions of the simplest 5-dimensional Kaluza-Klein theory using Wald’s formalism. We show how the electric work term present in the 4-dimensional first law of black-hole thermodynamics arises in the purely gravitational 5-dimensional framework. In particular, we find an interesting geometric interpretation of the 4-dimensional electrostatic potential similar to the angular velocity in rotating black holes. Furthermore, we show how the momentum map equation arises from demanding compatibility between the timelike Killing vector of the black-hole solution and the spatial Killing vector of the 5-dimensional background.

Publisher

Springer Science and Business Media LLC

Subject

Nuclear and High Energy Physics

Reference47 articles.

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4. N. Straumann, On Pauli’s invention of nonAbelian Kaluza-Klein theory in 1953, in the proceedings of the 9th Marcel Grossmann Meeting on Recent Developments in Theoretical and Experimental General Relativity, Gravitation and Relativistic Field Theories (MG 9), Rome Italy, July 2–9 (2000) p. 1063–1066 [gr-qc/0012054] [INSPIRE].

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