Gravitational acceleration of relativistic particles at finite temperature

Starting from the explicit expression of a generalized energy-momentum tensor, representing the effective source of gravity at finite temperature, it is shown that, in the case of a weak, static field and in the low-temperature limit, the thermal corrections to the gravitational acceleration of a relativistic test particle do not depend on its kinetic energy, and that the only effect is a constant, mass-dependent shift of the gravitational to inertial mass ratio, just as in the case, previously discussed, of nonrelativistic test bodies