Mathematical Physics, Analysis and Geometry

, Volume 15, Issue 1, pp 61–83

Grand Canonical Ensembles in General Relativity

Authors

    • Department of Mathematics and Interdisciplinary Research Institute for the SciencesCalifornia State University Northridge
  • Wei-Shih Yang
    • Department of MathematicsTemple University
Article

DOI: 10.1007/s11040-011-9103-5

Cite this article as:
Klein, D. & Yang, W. Math Phys Anal Geom (2012) 15: 61. 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, 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.

Keywords

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

Copyright information

© Springer Science+Business Media B.V. 2012