The Dirac propagator in the extreme Kerr metric

TL;DR

This paper derives an integral representation for the Dirac propagator in the extreme Kerr spacetime, facilitating analysis of fermionic fields in this rotating black hole background.

Contribution

It provides the first explicit integral formula for the Dirac propagator in the extreme Kerr metric, advancing mathematical understanding of fermions in rotating black holes.

Findings

Explicit integral representation of the Dirac propagator.

Framework for analyzing fermionic fields in extreme Kerr spacetime.

Potential applications to quantum field theory in curved spacetime.

Abstract

Starting with the Dirac equation in the extreme Kerr metric we derive an integral representation for the propagator of solutions of the Cauchy problem with initial data in the class of smooth compactly supported functions.