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 \(L^\infty_{\mbox{\scriptsize{loc}}}\) 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 [4].
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Received: 20 August 2001 / Accepted: 22 January 2002
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ID="*"Present address: NWF I – Mathematik, Universität Regensburg, 93040 Regensburg, Germany.¶E-mail: felix.finster@mathematik.uni-regensburg.de
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ID="**"Research supported by NSERC grant # RGPIN 105490-1998.
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ID="***"Research supported in part by the NSF, Grant No. DMS-0103998.
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ID="****"Research supported in part by the NSF, Grant No. 33-585-7510-2-30.
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Finster, F., Kamran, N., Smoller, J. et al. Decay Rates and Probability Estimates¶for Massive Dirac Particles¶in the Kerr–Newman Black Hole Geometry. Commun. Math. Phys. 230, 201–244 (2002). https://doi.org/10.1007/s002200200648
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DOI: https://doi.org/10.1007/s002200200648