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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 thedoi:10.1103/physrevd.49.4196 pmid:10017424 fatcat:lhnrjd3n2vcb7nbov2c57vcd3m