Quasi-normal modes and exponential energy decay for the Kerr-de Sitter black hole

Mar, 2010
26 pages
Published in:
  • Commun.Math.Phys. 306 (2011) 119-163
e-Print:

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Abstract: (arXiv)
We provide a rigorous definition of quasi-normal modes for a rotating black hole. They are given by the poles of a certain meromorphic family of operators and agree with the heuristic definition in the physics literature. If the black hole rotates slowly enough, we show that these poles form a discrete subset of the complex plane. As an application we prove that the local energy of linear waves in that background decays exponentially once orthogonality to the zero resonance is imposed.
Note:
  • 48+eps pages, 5 figures/ changes in presentation made and references added
  • black hole: rotation
  • quasinormal mode
  • operator
  • pole
  • black hole: Kerr
  • de Sitter
  • holomorphic
  • semiclassical
  • boundary condition