The wave equation on axisymmetric stationary black hole backgrounds

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

Understanding the behaviour of linear waves on black hole backgrounds is a central problem in general relativity, intimately connected with the nonlinear stability of the black hole spacetimes themselves as solutions to the Einstein equations-a major open question in the subject. Nonetheless, it is only very recently that even the most basic boundedness and quantitative decay properties of linear waves have been proven in a suitably general class of black hole exterior spacetimes. This talk will review our current mathematical understanding of waves on black hole backgrounds, beginning with the classical boundedness theorem of Kay and Wald on exactly Schwarzschild exteriors and ending with very recent boundedness and decay theorems (proven in collaboration with Igor Rodnianski) on a wider class of spacetimes. This class of spacetimes includes in particular slowly rotating Kerr spacetimes, but in the case of the boundedness theorem is in fact much larger, encompassing general axisymmetric stationary spacetimes whose geometry is sufficiently close to Schwarzschild and whose Killing fields span the null generator of the horizon.

Original languageEnglish (US)
Title of host publicationSpace Plasma Physics - School and Workshop on Space Plasma Physics
Pages19-38
Number of pages20
DOIs
StatePublished - 2009
Externally publishedYes
EventSpanish Relativity Meeting 2008 - Salamanca, Spain
Duration: Sep 15 2008Sep 19 2008

Publication series

NameAIP Conference Proceedings
Volume1122
ISSN (Print)0094-243X
ISSN (Electronic)1551-7616

Other

OtherSpanish Relativity Meeting 2008
CountrySpain
CitySalamanca
Period9/15/089/19/08

All Science Journal Classification (ASJC) codes

  • Physics and Astronomy(all)

Keywords

  • Black holes
  • Kerr metric
  • Wave equation

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  • Cite this

    Dafermos, M. (2009). The wave equation on axisymmetric stationary black hole backgrounds. In Space Plasma Physics - School and Workshop on Space Plasma Physics (pp. 19-38). (AIP Conference Proceedings; Vol. 1122). https://doi.org/10.1063/1.3141255