Universal analytic dependence of the stress-energy tensor at thermodynamic equilibrium in curved space-time

TL;DR

This paper demonstrates that the analytic part of the stress-energy tensor at thermodynamic equilibrium in curved space-time is universal and expressible in a covariant form, based on exact solutions and analytic distillation.

Contribution

It shows the universality and covariant form of the analytic gradient expansion of the stress-energy tensor in various curved space-times.

Findings

The analytic part has a finite number of terms in specific space-times.

Non-analytic terms depend on boundary conditions and global properties.

Universality extends to any quantum field theory on curved backgrounds.

Abstract

The mean value of the stress-energy tensor of a given quantum field theory at global thermodynamic equilibrium in a curved space-time can be expressed in terms of the derivatives of the Killing four-temperature field and the derivatives of the metric tensor. Its asymptotic expansion about zero includes an analytic part made of integer powers of these derivatives - corresponding to the so-called gradient expansion - as well as non-perturbative corrections. By using available exact solutions for the free real massless scalar field, we show that in the case of Minkowski, de Sitter, anti-de Sitter, and closed Einstein universe, the analytic part - obtained through the procedure of analytic distillation - has a finite number of terms and it is the same once expressed in a covariant form. On the other hand, non-universal terms are non-analytic in these derivatives and correspond to boundary conditions or to specific global properties of the space-time. We argue that the universality of the analytic part extends to any quantum field theory on a curved background.