The black hole stability problem for linear scalar perturbations

Details The black hole stability problem for linear scalar perturbations The black hole stability problem for linear scalar perturbations

2010-10-25

arxiv.org/abs/1010.5137v1

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

48 pages, 5 figures, to appear in Proceedings of the 12 Marcel Grossmann Meeting

Scientific paper

We review our recent work on linear stability for scalar perturbations of Kerr spacetimes, that is to say, boundedness and decay properties for solutions of the scalar wave equation \Box_g{\psi} = 0 on Kerr exterior backgrounds. We begin with the very slowly rotating case |a| \ll M, where first boundedness and then decay has been shown in rapid developments over the last two years, following earlier progress in the Schwarzschild case a = 0. We then turn to the general subextremal range |a| < M, where we give here for the first time the essential elements of a proof of definitive decay bounds for solutions {\psi}. These developments give hope that the problem of the non-linear stability of the Kerr family of black holes might soon be addressed. This paper accompanies a talk by one of the authors (I.R.) at the 12th Marcel Grossmann Meeting, Paris, June 2009.

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