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Decay for solutions of the wave equation on Kerr exterior spacetimes. III: The full subextremalcase \(|a| < M\). (English) Zbl 1347.83002

Authors’ abstract: This paper concludes the series begun in [the first and the second author, “Decay for solutions of the wave equation on Kerr exterior spacetimes I–II: the cases \(|a| \ll M\) or axisymmetry”, Preprint, arXiv:1010.5132], providing the complete proof of definitive boundedness and decay results for the scalar wave equation on Kerr backgrounds in the general subextremal \(|a|< M\) case without symmetry assumptions. The essential ideas of the proof (together with explicit constructions of the most difficult multiplier currents) have been announced in our survey [the first and the second author, “The black hole stability problem for linear scalar perturbations”, in: P. Exner (ed.), XVIth International Congress on Mathematical Physics. Singapore: World Scientific. 421–433 (2011), arXiv:1010.5137]. Our proof appeals also to the quantitative mode-stability proven in [the third author, Ann. Henri Poincaré 16, No. 1, 289–345 (2015; Zbl 1308.83104)], together with a streamlined continuity argument in the parameter \(a\), appearing here for the first time. While serving as Part III of a series, this paper repeats all necessary notation so that it can be read independently of previous work.

MSC:

83-02 Research exposition (monographs, survey articles) pertaining to relativity and gravitational theory
35L05 Wave equation
35Q75 PDEs in connection with relativity and gravitational theory
83C05 Einstein’s equations (general structure, canonical formalism, Cauchy problems)
83C15 Exact solutions to problems in general relativity and gravitational theory
83C57 Black holes
83C25 Approximation procedures, weak fields in general relativity and gravitational theory

Citations:

Zbl 1308.83104
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References:

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