Thermal Effective Lagrangian of Static Gravitational Fields

TL;DR

This paper derives a closed-form expression for the thermal effective Lagrangian of static gravitational fields interacting with thermal fields across various space-time dimensions, using imaginary time formalism and static field equivalence.

Contribution

It introduces a novel method to compute the thermal effective Lagrangian for static gravitational fields in arbitrary dimensions, combining imaginary time formalism with static field equivalence.

Findings

Closed-form expression for thermal effective Lagrangian in arbitrary dimensions

Utilization of imaginary time formalism for gravitational interactions

Application of static and space-time independent field equivalence

Abstract

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.