Timelike Killing Fields and Relativistic Statistical Mechanics

Abstract

For spacetimes with timelike Killing fields, we introduce a "Fermi-Walker-Killing" coordinate system and use it to prove a Liouville Theorem for an appropriate volume element of phase space for a statistical mechanical system of particles. We derive an exact relativistic formula for the Helmholtz free energy of an ideal gas and compare it, for a class of spacetimes, to its Newtonian analog, derived both independently and as the Newtonian limit of our formula. We also find the relativistic thermodynamic equation of state. Specific examples are given in Kerr spacetime.

This version contains minor corrections, additional discussion, and will appear in Classical and Quantum Gravity

References in corpus (3)

• General Transformation Formulas for Fermi-Walker Coordinates
• Statistical mechanics of generally covariant quantum theories: A Boltzmann-like approach
• A Statistical Mechanical Problem in Schwarzschild Spacetime

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• Grand canonical ensembles in general relativity
• General Relativistic Center-of-Mass Coordinates for Composite Quantum Particles