Heat kernels and thermodynamics in Rindler space

TL;DR

This paper investigates the proper method to compute quantum corrections to Rindler space entropy, emphasizing the importance of using a topology without conical singularities for accurate temperature dependence.

Contribution

It demonstrates that accurate quantum entropy calculations require heat kernels in topologies without conical singularities, correcting previous approaches and clarifying regularization ambiguities.

Findings

Heat kernel on a cone does not give correct temperature dependence.

Heat kernel in topology without conical singularity matches other methods.

Regularization ambiguities are discussed and clarified.

Abstract

We point out that using the heat kernel on a cone to compute the first quantum correction to the entropy of Rindler space does not yield the correct temperature dependence. In order to obtain the physics at arbitrary temperature one must compute the heat kernel in a geometry with different topology (without a conical singularity). This is done in two ways, which are shown to agree with computations performed by other methods. Also, we discuss the ambiguities in the regularization procedure.