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Bulletin of the American Mathematical Society

The Bulletin publishes expository articles on contemporary mathematical research, written in a way that gives insight to mathematicians who may not be experts in the particular topic. The Bulletin also publishes reviews of selected books in mathematics and short articles in the Mathematical Perspectives section, both by invitation only.

ISSN 1088-9485 (online) ISSN 0273-0979 (print)

The 2020 MCQ for Bulletin of the American Mathematical Society is 0.84.

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Linear waves in the Kerr geometry: A mathematical voyage to black hole physics
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by Felix Finster, Niky Kamran, Joel Smoller and Shing-Tung Yau PDF
Bull. Amer. Math. Soc. 46 (2009), 635-659 Request permission

Abstract:

This paper gives a survey of wave dynamics in the Kerr space-time geometry, the mathematical model of a rotating black hole in equilibrium. After a brief introduction to the Kerr metric, we review the separability properties of linear wave equations for fields of general spin $s=0,\frac {1}{2}, 1, 2$, corresponding to scalar, Dirac, electromagnetic fields and linearized gravitational waves. We give results on the long-time dynamics of Dirac and scalar waves, including decay rates for massive Dirac fields. For scalar waves, we give a rigorous treatment of superradiance and describe rigorously a mechanism of energy extraction from a rotating black hole. Finally, we discuss the open problem of linear stability of the Kerr metric and present partial results.
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Additional Information
  • Felix Finster
  • Affiliation: NWF I – Mathematik, Universität Regensburg, 93040 Regensburg, Germany
  • Email: Felix.Finster@mathematik.uni-regensburg.de
  • Niky Kamran
  • Affiliation: Department of Mathematics and Statistics, McGill University, Montreal, Quebec, H3A 2K6 Canada
  • MR Author ID: 97615
  • Email: nkamran@math.mcgill.ca
  • Joel Smoller
  • Affiliation: Department of Mathematics, University of Michigan, Ann Arbor, Michigan 48109
  • Email: smoller@umich.edu
  • Shing-Tung Yau
  • Affiliation: Department of Mathematics, Harvard University, Cambridge, Massachusetts 01238
  • MR Author ID: 185480
  • ORCID: 0000-0003-3394-2187
  • Email: yau@math.harvard.edu
  • Received by editor(s): January 9, 2008
  • Received by editor(s) in revised form: August 11, 2008, and February 18, 2009
  • Published electronically: May 5, 2009
  • Additional Notes: The first author’s research was supported in part by the Deutsche Forschungsgemeinschaft.
    The second author’s research supported by NSERC grant RGPIN 105490-2004.
    The third author’s research was supported in part by the National Science Foundation, Grant No. DMS-0603754.
    The fourth author’s research was supported in part by the NSF, Grant No. 33-585-7510-2-30.
  • © Copyright 2009 American Mathematical Society
  • Journal: Bull. Amer. Math. Soc. 46 (2009), 635-659
  • MSC (2000): Primary 83C57, 35L15, 83C55
  • DOI: https://doi.org/10.1090/S0273-0979-09-01258-0
  • MathSciNet review: 2525736