Entropy of Quantum Fields for Nonextreme Black Holes in the Extreme Limit

Abstract

Nonextreme black hole in a cavity within the framework of the canonical or grand canonical ensemble can approach the extreme limit with a finite temperature measured on a boundary located at a finite proper distance from the horizon. In spite of this finite temperature, it is shown that the one-loop contribution $S_q$of quantum fields to the thermodynamic entropy due to equilibrium Hawking radiation vanishes in the limit under consideration. The same is true for the finite temperature version of the Bertotti-Robinson spacetime into which a classical Reissner-Nordström black hole turns in the extreme limit. The result $S_q=0$ is attributed to the nature of a horizon for the Bertotti-Robinson spacetime.

11 pages, ReVTeX, no figures. New references added, discussion expanded, presentation and English improved. Accepted for publication in Phys. Rev. D

References in corpus (2)

• The ``Nernst Theorem'' and Black Hole Thermodynamics
• Geometry of nonextreme black holes near the extreme state

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