Gravitational energy, gravitational pressure, and the thermodynamics of a charged black hole in teleparallel gravity

Abstract

We investigate, in the case of a Reissner-Nordström black hole, the definitions of gravitational energy and gravitational pressure that naturally arise in the framework of the Teleparallel Equivalent of General Relativity. In particular, we calculate the gravitational energy enclosed by the event horizon of the black hole, E, and the radial pressure over it, p. With these quantities we then analyse the thermodynamic relation dE + pdV (as p turns out to be a density, dV is actually given by dV = dr dθdϕ, in spherically-type coordinates). We compare the latter with the standard first law of black hole dynamics. Also, by identifying TdS = dE + pdV, we comment on a possible modification of the standard, Bekenstein-Hawking entropy-area relation due to gravitational energy and gravitational pressure of the black hole. The infinitesimal variations in question refer to the Penrose process for a Reissner-Nordström black hole.

20 pages, version to match the one which appeared in Physical Review D

References in corpus (8)

• The teleparallel equivalent of general relativity
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• Covariance properties and regularization of conserved currents in tetrad gravity
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Cited by in corpus (5)

• Teleparallel Gravity: From Theory to Cosmology
• On the hadron mass decomposition
• Black holes and Boyle's law -- the thermodynamics of the cosmological constant
• Gravitational energy and radiation of a charged black hole
• Gravitational Pressure, apparent horizon and thermodynamics of FLRW universe in the teleparallel gravity