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MiS Preprint
57/2001
Decay rates and probability estimates for massive Dirac particles in the Kerr-Newman black hole geometry
Felix Finster, Niky Kamran, Joel Smoller and Shing-Tung Yau
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 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.
