Mathematical Physics, Analysis and Geometry

, Volume 15, Issue 1, pp 61-83

First online:

Grand Canonical Ensembles in General Relativity

  • David KleinAffiliated withDepartment of Mathematics and Interdisciplinary Research Institute for the Sciences, California State University Northridge Email author 
  • , Wei-Shih YangAffiliated withDepartment of Mathematics, Temple University

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We develop a formalism for general relativistic, grand canonical ensembles in space-times with timelike Killing fields. Using that, 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.


Relativistic Gibbs state Fermi coordinates Grand canonical ensemble Ideal gas Anti-de Sitter space De-Sitter space Einstein static universe Kerr space-time

Mathematics Subject Classification (2010)

82B21 83C15 83F05