Finite Temperature Effects for Massive Fields in D-dimensional Rindler-like Spaces

TL;DR

This paper investigates quantum corrections to free energy for massive fields in D-dimensional Rindler-like spaces using zeta-function regularization, revealing divergence structures and recurrence relations across dimensions.

Contribution

It introduces a detailed analysis of horizon divergences and recurrence relations for quantum corrections in Rindler-like geometries, expanding understanding of thermodynamics in curved spacetimes.

Findings

Derived general form of horizon divergences in free energy.

Established recurrence relations linking different dimensions.

Analyzed specific cases like Rindler space and high-mass black holes.

Abstract

The first quantum corrections to the free energy for massive fields in $D$-dimensional space-times of the form $\R\times\R^+\times\M^{N-1}$, where $D=N+1$ and $\M^{N-1}$ is a constant curvature manifold, is investigated by means of the $\zeta$-function regularization. It is suggested that the nature of the divergences, which are present in the thermodynamical quantities, might be better understood making use of the conformal related optical metric and associated techniques. The general form of the horizon divercences of the free energy is obtained as a function of free energy densities of fields having negative square masses (absence of the gap in the Laplace operator spectrum) on ultrastatic manifolds with hyperbolic spatial section $H^{N-2n}$ and of the Seeley-DeWitt coefficients of the Laplace operator on the manifold $\M^{N-1}$. Furthermore, recurrence relations are found relating higher and lower dimensions. The cases of Rindler space, where $\M^{N-1}=\R^{N-1}$ and very massive $D$-dimensional black holes, where $\M^{N-1}=S^{N-1}$ are treated as examples. The renormalization of the internal energy is also discussed.