Partition function of massless scalar field in Schwarzschild background

TL;DR

This paper develops a method to compute the partition function of a massless scalar field in Schwarzschild spacetime using a thermal zeta function approach, removing regularization ambiguities and addressing trace anomaly issues.

Contribution

It explicitly calculates the coincidence limit of the zeta function, enabling application to specific problems like the Schwarzschild background.

Findings

Partition function is independent of regularization constants in even dimensions.

Trace anomaly effects are effectively removed using the thermal zeta function approach.

Explicit expression for the coincidence limit is derived for practical calculations.

Abstract

Using thermal value of zeta function instead of zero temperature, the partition function of quantized fields in arbitrary stationary backgrounds was found to be independent of undetermined regularization constant in even-dimension and the long drawn problem associated with the trace anomaly effect had been removed. Here, we explicitly calculate the expression for the coincidence limit so that the technique may be applied in some specific problems. A particular problem dealt with here is to calculate the partition function of massless scalar field in Schwarzschild background.