MiS Preprint Repository

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 $L_{loc}^{\mathrm{\infty }}$ 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
F. Finster, N. Kamran, J. Smoller and S.-T. Yau, "The long-time dynamics of Dirac particles in the Kerr-Newman black hole geometry," gr-qc/0005088.