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Communications in Mathematical Physics

, Volume 230, Issue 2, pp 201–244 | Cite as

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

  • F. Finster
  • N. Kamran
  • J. Smoller
  • S.-T. Yau

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].

Keywords

Wave Function Angular Momentum Initial Data Decay Rate Cauchy Problem 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  • F. Finster
    • 1
  • N. Kamran
    • 2
  • J. Smoller
    • 3
  • S.-T. Yau
    • 4
  1. 1.Max Planck Institute for Mathematics in the Sciences, Inselstr. 22–26, 04103 Leipzig, Germany.¶E-mail: Felix.Finster@mis.mpg.deDE
  2. 2.Department of Math. and Statistics, McGill University, Montréal, Québec, Canada, H3A 2K6.¶E-mail: nkamran@math.McGill.CAUS
  3. 3.Mathematics Department, The University of Michigan, Ann Arbor, MI 48109, USA.¶E-mail: smoller@umich.eduUS
  4. 4.Mathematics Department, Harvard University, Cambridge, MA 02138, USA.¶E-mail: yau@math.harvard.eduUS

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