Thermal partition function of photons and gravitons in a Rindler wedge

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 $s\ge 1$ 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.

arXiv comment29 pages, RevTeX, no figures. Minor errors corrected and a few comments changed since first submission. To be published on Phys.Rev.D

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• Direct $\zeta$-function approach and renormalization of one-loop stress tensors in curved spacetimes
• Dynamical Chiral Symmetry Breaking and its Restoration for an Accelerated Observer
• Thermodynamics of scalar fields in Kerr's geometry
• Optical Approach for the Thermal Partition Function of Photons
• Generalized Gravitational Entropy of Interacting Scalar Field and Maxwell Field
• Geometric Entropy and Curvature Coupling in Conical Spaces: zeta Function Approach
• Canonical Quantization of the U(1) Gauge Field in the Rindler Coordinates