Temperature oscillations of a gas in circular geodesic motion in the Schwarzschild field

TL;DR

This paper studies temperature oscillations of a gas in circular geodesic motion within Schwarzschild spacetime, revealing oscillations at twice the frequency of test-particle motion, with applications to planetary and astrophysical objects.

Contribution

It demonstrates that a gas in equilibrium exhibits temperature oscillations at double the test-particle frequency in Schwarzschild spacetime, extending Tolman's law to dynamic thermodynamic quantities.

Findings

Temperature oscillates with twice the frequency of particle motion.

Oscillations are observed in both weak and strong gravitational fields.

Implications for thermodynamics in astrophysical environments.

Abstract

We investigate a Boltzmann gas at equilibrium with its center of mass moving on a circular geodesics in the Schwarzschild field. As a consequence of Tolman's law we find that a central comoving observer measures oscillations of the temperature and of other thermodynamic quantities with twice the frequencies that are known from test-particle motion. We apply this scheme to the gas dynamics in the gravitational fields of the planets of the Solar System as well as to strong-field configurations of neutron stars and black holes.