320 research outputs found
The black hole stability problem for linear scalar perturbations
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.Comment: 48 pages, 5 figures, to appear in Proceedings of the 12 Marcel
Grossmann Meetin
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