The generalized Heun equation in QFT in curved space-times

TL;DR

This paper explores how the generalized Heun equation (GHE) applies to Quantum Field Theory in curved space-times, specifically relating it to the Dirac equation in Kerr-Newman and Reissner-Nordström metrics.

Contribution

It demonstrates the relevance of GHE in describing quantum fields in curved backgrounds, linking it to specific solutions in black hole spacetimes.

Findings

Radial Dirac equation in Kerr-Newman relates to GHE

Static perturbations in Reissner-Nordström relate to GHE

Highlights the role of GHE in quantum gravity contexts

Abstract

In this article we give a brief outline of the applications of the generalized Heun equation (GHE) in the context of Quantum Field Theory in curved space-times. In particular, we relate the separated radial part of a massive Dirac equation in the Kerr-Newman metric and the static perturbations for the non-extremal Reissner-Nordstr\"{o}m solution to a GHE.