Kabat’s Surface Terms in the Zeta-function Approach

The thermal partition functions of photons in any covariant gauge and gravitons in the harmonic gauge, propagating in a Rindler wedge, are computed using a local zeta-function approach. The results are discussed in relation to the quantum corrections to the black hole entropy. The correct leading order temperature dependence T 4 is obtained in both cases. For the photons, it is confirmed the existence of a surface term giving a negative contribution to the entropy, as earlier obtained by D.Kabat, but this term is shown to be gauge-dependent in the four dimensional case and therefore discarded. It is argued that similar terms could appear dealing with any integer spin s ≥ 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.