High-temperature expansion of the one-loop free energy of a scalar field on a curved background

TL;DR

This paper derives the high-temperature expansion of the one-loop free energy for a scalar field in a curved, stationary spacetime, revealing new corrections and anomalies related to the metric's non-static nature.

Contribution

It provides explicit formulas for the high-temperature expansion, including divergent and finite parts, generalizing previous results to non-static backgrounds and exploring related anomalies.

Findings

Leading correction to Planck law is nonzero for massless conformal scalar due to non-static metric

Explicit expression for energy-time anomaly is obtained

Interrelation between energy-time and conformal anomalies is established

Abstract

The complete form of the high-temperature expansion of the one-loop contribution to the free energy of a scalar field on a stationary gravitational background is derived. The explicit expressions for the divergent and finite parts of the high-temperature expansion in a three-dimensional space without boundaries are obtained. These formulas generalize the known one for the stationary spacetime. In particular, we confirm that for a massless conformal scalar field the leading correction to the Planck law proportional to the temperature squared turns out to be nonzero due to non-static nature of the metric. The explicit expression for the so-called energy-time anomaly is found. The interrelation between this anomaly and the conformal (trace) anomaly is established. The natural simplest Lagrangian for the "Killing vector field" is given.