Grand canonical ensembles in general relativity

TL;DR

This paper develops a formalism for grand canonical ensembles in general relativity, deriving ideal gas laws dependent on space-time geometry, and analyzes their Newtonian limits and phase transition properties.

Contribution

It introduces a new formalism for relativistic grand canonical ensembles and explores their thermodynamic properties in various space-times.

Findings

Ideal gas laws depend on space-time geometry

Systematic method for Newtonian limits in Kerr space-time

Proved uniqueness of Gibbs measure and absence of phase transitions in anti-de Sitter space

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.