A Statistical Mechanical Problem in Schwarzschild Spacetime

TL;DR

This paper derives the statistical mechanics of an ideal gas in Schwarzschild spacetime using Fermi coordinates, connecting relativistic and Newtonian limits, and discusses extensions to non-ideal gases.

Contribution

It introduces a method to compute the partition function for gases in curved spacetime and validates it by recovering known physical laws in specific limits.

Findings

Recovered Newtonian gas law with tidal forces

Recovered special relativistic gas law at large radii

Proposed extension to non-ideal gases

Abstract

We use Fermi coordinates to calculate the canonical partition function for an ideal gas in a circular geodesic orbit in Schwarzschild spacetime. To test the validity of the results we prove theorems for limiting cases. We recover the Newtonian gas law subject only to tidal forces in the Newtonian limit. Additionally we recover the special relativistic gas law as the radius of the orbit increases to infinity. We also discuss how the method can be extended to the non ideal gas case.