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.
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Collas, P., Klein, D. A statistical mechanical problem in Schwarzschild spacetime. Gen Relativ Gravit 39, 737–755 (2007). https://doi.org/10.1007/s10714-007-0416-4
- Ideal gas
- Schwarzschild spacetime
- Fermi coordinates
- Statistical mechanics