Thermal matter and radiation in a gravitational field

TL;DR

This paper analyzes how matter and radiation at finite temperatures influence gravitational polarization, deriving explicit formulas and exploring thermal masses of graviton modes.

Contribution

It provides explicit next-to-leading order matter contributions and an exact radiation contribution to the gravitational polarization tensor at finite temperature.

Findings

Explicit matter contribution at $T^2$ order

Exact radiation contribution in terms of Riemann zeta functions

Derived general expression for the physical polarization tensor

Abstract

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.