Scattering of massive Dirac fields on the Schwarzschild black hole spacetime

TL;DR

This paper develops a scattering theory for massive Dirac fields around Schwarzschild black holes, introducing a matrix phase shift to account for long-range mass effects and establishing the existence of modified wave operators.

Contribution

It presents a novel scattering framework for massive Dirac fields in curved spacetime, incorporating a matrix phase shift to handle positive and negative energy components.

Findings

Existence of modified wave operators established.

Logarithmic phase shift accounts for long-range mass effects.

Matrix operator form due to positive and negative energy components.

Abstract

With a generally covariant equation of Dirac fields outside a black hole, we develop a scattering theory for massive Dirac fields. The existence of modified wave operators at infinity is shown by implementing a time-dependent logarithmic phase shift from the free dynamics to offset a long-range mass term. The phase shift we obtain is a matrix operator due to the existence of both positive and negative energy wave components.