Decay Rates and Probability Estimates for Massive Dirac Particles in the Kerr-Newman Black Hole Geometry

TL;DR

This paper analyzes the decay rates and escape probabilities of massive Dirac particles in Kerr-Newman black hole spacetime, establishing decay at a specific rate and conditions for escape or capture.

Contribution

It provides the first detailed decay rate and escape probability estimates for Dirac particles in Kerr-Newman geometry, extending previous analyses of wave equations in black hole backgrounds.

Findings

Decay rate of t^{-5/6} for Dirac wave functions

Conditions under which particles escape or are captured

Explicit formula for escape probability p

Abstract

The Cauchy problem is considered for the massive Dirac equation in the non-extreme Kerr-Newman geometry, for smooth initial data with compact support outside the event horizon and bounded angular momentum. We prove that the Dirac wave function decays in L^\infty_loc at least at the rate t^{-5/6}. For generic initial data, this rate of decay is sharp. We derive a formula for the probability p that the Dirac particle escapes to infinity. For various conditions on the initial data, we show that p=0,1 or 0<p<1. The proofs are based on a refined analysis of the Dirac propagator constructed in gr-qc/0005088.