Scattering for massive Dirac fields on the Kerr metric

TL;DR

This paper develops a time-dependent scattering theory for massive Dirac particles around Kerr black holes, explicitly computing wave operators and accounting for gravitational long-range effects.

Contribution

It introduces a novel time-dependent scattering framework for Dirac fields in Kerr spacetime, including explicit wave operator formulas with a logarithmic phase shift.

Findings

Explicit wave operators for Dirac fields in Kerr spacetime

Implementation of a logarithmic phase shift for long-range gravitational effects

Analytical expressions for scattering operators provided

Abstract

Starting with the Dirac equation outside the event horizon of a non-extreme Kerr black hole, we develop a time-dependent scattering theory for massive Dirac particles. The explicit computation of the modified wave operators at infinity is done by implementing a time-dependent logarithmic phase shift from the free dynamics to offset the long range term in the full Hamiltonian due to the presence of the gravitational force. Analytical expressions for the wave operators are also given.