Grand canonical ensembles in general relativity
Mathematical Physics
2012-03-19 v2 General Relativity and Quantum Cosmology
math.MP
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.
Cite
@article{arxiv.1009.3846,
title = {Grand canonical ensembles in general relativity},
author = {David Klein and Wei-Shih Yang},
journal= {arXiv preprint arXiv:1009.3846},
year = {2012}
}
Comments
This manuscript includes minor additions to the original, that appear in the published version. arXiv admin note: substantial text overlap with arXiv:0810.1776