Decay rates and probability estimates for massive Dirac particles in the Kerr-Newman black hole geometry

The Cauchy problem is considered for the massive Dirac equation in the non-extreme Keff-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(infinity) 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 < The proofs are based on a refined analysis of the Dirac propagator constructed in [4].