Thermal Effective Lagrangian of Static Gravitational Fields
  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. 
F T Brandt and J B Siqueira
hep-th