Kabat's Surface Terms in the Zeta-Function approach

TL;DR

The paper reevaluates Kabat’s surface terms within a local zeta-function framework for quantum fields in a Rindler wedge to assess their impact on black-hole entropy corrections. It demonstrates that the electromagnetic zeta function splits into a scalar-like part plus a gauge-dependent surface term, which is discarded to maintain gauge invariance, yielding physically sensible thermodynamic quantities. The authors extend the analysis to higher spins by conjecturing analogous surface terms on M × R^2 with conical singularities and verify the graviton case, obtaining a result consistent with twice the scalar case after removing surface contributions. These findings clarify the role of surface terms in quantum corrections to entropy and propose a broader, testable framework for higher-spin fields in curved backgrounds.

Abstract

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 relation with the surface terms previously obtained by D. Kabat is studied. The results are discussed in relation to the quantum corrections to the black hole entropy.