We compute the effective Lagrangian of static gravitational fields interacting with thermal fields. Our approach employs the usual imaginary time formalism as well as the equivalence between the static and space-time independent external gravitational fields. This allows to obtain a closed form expression for the thermal effective Lagrangian in $d$ space-time dimensions.

• Received 7 December 2011

DOI:https://doi.org/10.1103/PhysRevD.85.067701