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

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.

42 pages, 3 figures (published version)

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• Asymptotic tails of massive scalar fields in Schwarzschild background
• Asymptotic power-law tails of massive scalar fields in Reissner-Nordström background

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