Quantum Corrections to the Entropy for Higher Spin Fields in Hyperbolic Space

TL;DR

This paper computes one-loop quantum corrections to entropy for higher spin fields in hyperbolic space, using zeta regularization, with implications for Rindler and black hole spacetimes.

Contribution

It provides a method to calculate quantum entropy corrections for arbitrary spin fields in hyperbolic space and relates these results to Rindler and black hole geometries.

Findings

Finite entropy corrections obtained via zeta regularization.

Results applicable to conformally invariant fields in Rindler space.

Addresses the infinite area problem in entropy calculations.

Abstract

We calculate the one-loop corrections to the free energy and to the entropy for fields with arbitrary spins in the space $S^1\otimes H^N$. For conformally invariant fields by means of a conformal transformation of the metric the results are valid in Rindler space with $D=N+1$ dimensions. We use the zeta regularization technique which yields an ultraviolet finite result for the entropy per unit area. The problem of the infinite area factor in the entropy which arises equally in Rindler space and in the black hole background is addressed in the light of a factor space $H^N/\Gamma$.