Thermal partition function of photons and gravitons in a Rindler wedge

TL;DR

This paper calculates the thermal partition functions for photons and gravitons in a Rindler wedge, confirming the temperature dependence and addressing gauge-dependent surface terms affecting entropy calculations.

Contribution

It provides a gauge-invariant computation of photon and graviton partition functions in a Rindler wedge using local ζ-function regularization, clarifying the role of surface terms.

Findings

Planckian $T^4$ temperature dependence confirmed

Surface terms affecting entropy are gauge dependent and discarded

Results have implications for quantum corrections to black hole entropy

Abstract

The thermal partition function of photons in any covariant gauge and gravitons in the harmonic gauge, propagating in a Rindler wedge, are computed using a local $\zeta$-function regularization approach. The correct Planckian leading order temperature dependence $T^4$ is obtained in both cases. For the photons, the existence of a surface term giving a negative contribution to the entropy is confirmed, as earlier obtained by Kabat, but this term is shown to be gauge dependent in the four-dimensional case and, therefore is discarded. It is argued that similar terms could appear dealing with any integer spin $s\geq 1$ in the massless case and in more general manifolds. Our conjecture is checked in the case of a graviton in the harmonic gauge, where different surface terms also appear, and physically consistent results arise dropping these terms. The results are discussed in relation to the quantum corrections to the black hole entropy.