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Generalized Hawking–Page phase transition

Parthasarathi Majumdar

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The issue of radiant spherical black holes being in stable thermal equilibrium with their radiation bath is reconsidered. Using a simple equilibrium statistical mechanical analysis incorporating Gaussian thermal fluctuations in a canonical ensemble of isolated horizons, the heat capacity is shown to diverge at a critical value of the classical mass of the isolated horizon, given (in Planckian units) by the microcanonical entropy calculated using loop quantum gravity. The analysis reproduces the Hawking–Page phase transition discerned for anti-de Sitter black holes and generalizes it in the sense that nowhere is any classical metric made use of.


PACS

04.70.-s Physics of black holes

04.60.Pp Loop quantum gravity, quantum geometry, spin foams

05.20.Gg Classical ensemble theory

05.70.Ce Thermodynamic functions and equations of state

05.40.-a Fluctuation phenomena, random processes, noise, and Brownian motion

05.70.Fh Phase transitions: general studies

MSC

82B26 Phase transitions (general)

82B30 Statistical thermodynamics (See also 80-XX)

82B05 Classical equilibrium statistical mechanics (general)

83C57 Black holes

Subjects

Gravitation and cosmology

Statistical physics and nonlinear systems

Dates

Issue 7 (7 April 2007)

Received 15 January 2007

Published 13 March 2007



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