David Klein and Peter Collas 2009 Class. Quantum Grav. 26 045018 doi:10.1088/0264-9381/26/4/045018
David Klein1 and Peter Collas2
Show affiliationsFor spacetimes with timelike Killing fields, we introduce a 'Fermi–Walker–Killing' coordinate system and use it to prove a Liouville theorem for an appropriate volume element of phase space for a statistical mechanical system of particles. We derive an exact relativistic formula for the Helmholtz free energy of an ideal gas and compare it, for a class of spacetimes, to its Newtonian analog, derived both independently and as the Newtonian limit of our formula. We also find the relativistic thermodynamic equation of state. Specific examples are given in Kerr spacetime.
04.70.Dy Quantum aspects of black holes, evaporation, thermodynamics
82B05 Classical equilibrium statistical mechanics (general)
Issue 4 (21 February 2009)
Received 10 October 2008, in final form 18 November 2008
Published 3 February 2009
David Klein and Peter Collas 2009 Class. Quantum Grav. 26 045018
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