Grand canonical ensembles in general relativity
arXiv:1009.3846 · doi:10.1007/s11040-011-9103-5
Abstract
We develop a formalism for general relativistic, grand canonical ensembles in space-times with timelike Killing fields. Using that formalism we derive ideal gas laws, and show how they depend on the geometry of the particular space-times. A systematic method for calculating Newtonian limits is given for a class of these space-times, which is illustrated for Kerr space-time. In addition, we prove uniqueness of the infinite volume Gibbs measure, and absence of phase transitions for a class of interaction potentials in anti-de Sitter space-time.
This manuscript includes minor additions to the original, that appear in the published version. arXiv admin note: substantial text overlap with arXiv:0810.1776
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