David Klein, Wei-Shih Yang
Grand canonical ensembles in general relativity
(68K, latex)
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.