2001/07/31 by Felix Finster, Niky Kamran, Joel Smoller +2 · 2 citations
Mathematics · Physics and Astronomy · #Advanced Mathematical Physics Problems #Black Holes and Theoretical Physics #Cosmology and Gravitation Theories #gr-qc #math-ph #math.AP #math.MP
paper · pdf · doi:10.1007/s002200200648
published as Commun.Math.Phys. 230 (2002) 201-244 · 42 pages, 3 figures (published version)
arxiv created 2002/01/31 · openalex publication_date 2002/10/01 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/04
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^∞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.