Thermal matter and radiation in a gravitational field

We study the one-loop contributions of matter and radiation to the gravitational polarization tensor at finite temperatures. Using the analytically continued imaginary-time formalism, the contribution of matter is explicitly given to next-to-leading ($T^2$) order. We obtain an exact form for the contribution of radiation fields, expressed in terms of generalized Riemann $\zeta$ functions. A general expression is derived for the physical polarization tensor, which is independent of the parametrization of graviton fields. We investigate the effective thermal masses associated with the normal modes of the corresponding graviton self-energy.