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

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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.