Conformal scattering theory for the Dirac field on Kerr spacetime

TL;DR

This paper develops a conformal scattering theory for the massless Dirac equation on Kerr spacetime, utilizing conformal geometric methods and decay assumptions, applicable to Schwarzschild and slowly rotating Kerr black holes.

Contribution

It introduces a new conformal scattering framework for the Dirac field on Kerr spacetime, extending previous methods to rotating black holes under decay conditions.

Findings

Constructed a conformal scattering theory for Dirac fields on Kerr spacetime.

Validated the approach for Schwarzschild and slowly Kerr black holes with established decay.

Provides a foundation for analyzing Dirac fields in rotating black hole backgrounds.

Abstract

We investigate to construct a conformal scattering theory of the spin-$1/2$ massless Dirac equation on the Kerr spacetime by using the conformal geometric method and under an assumption on the pointwise decay of the Dirac field. In particular, our construction is valid in the exteriors of Schwarzschild and very slowly Kerr black hole spacetimes, where the pointwise decay was established.