The Long-Time Dynamics of Dirac Particles in the Kerr-Newman Black Hole Geometry

TL;DR

This paper analyzes the long-term behavior of Dirac particles in Kerr-Newman black hole spacetime, showing particles either fall into the black hole or escape to infinity over time.

Contribution

It provides an integral representation of the Dirac propagator in Kerr-Newman geometry and proves the asymptotic decay of particle probability in bounded regions.

Findings

Particles tend to escape to infinity or fall into the black hole over time.

The probability of finding the particle in any compact region tends to zero as time approaches infinity.

The paper establishes the long-time dynamics of Dirac particles in this black hole geometry.

Abstract

We consider the Cauchy problem for the massive Dirac equation in the non-extreme Kerr-Newman geometry outside the event horizon. We derive an integral representation for the Dirac propagator involving the solutions of the ODEs which arise in Chandrasekhar's separation of variables. It is proved that for initial data in L^\infty_loc near the event horizon with L^2 decay at infinity, the probability of the Dirac particle to be in any compact region of space tends to zero as t goes to infinity. This means that the Dirac particle must either disappear in the black hole or escape to infinity.