Communications in Mathematical Physics

, Volume 230, Issue 2, pp 201–244

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

DOI: 10.1007/s002200200648

Cite this article as:
Finster, F., Kamran, N., Smoller, J. et al. Commun. Math. Phys. (2002) 230: 201. doi: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 \(L^\infty_{\mbox{\scriptsize{loc}}}\) 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].

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