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
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Submission date: 29. Aug. 2001
published in: Communications in mathematical physics, 230 (2002) 2, p. 201-244
DOI number (of the published article): 10.1007/s002200200648
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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 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.