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

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

2001-07-28

arxiv.org/abs/gr-qc/0107094v2

Commun.Math.Phys. 230 (2002) 201-244

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

42 pages, 3 figures (published version)

Scientific paper

10.1007/s002200200648

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

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