TY - GEN
T1 - The black hole stability problem for linear scalar perturbations
AU - Dafermos, Mihalis
AU - Rodnianski, Igor
PY - 2012
Y1 - 2012
N2 - 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 equa- Tion gψ = 0 on Kerr exterior backgrounds (M, ga,M ). We begin with the very slowly rotating case |a| ≪ 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 ψ. These developments give hope that the problem of the non-linear stability of the Kerr family of black holes might soon be addressed.
AB - 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 equa- Tion gψ = 0 on Kerr exterior backgrounds (M, ga,M ). We begin with the very slowly rotating case |a| ≪ 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 ψ. These developments give hope that the problem of the non-linear stability of the Kerr family of black holes might soon be addressed.
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U2 - 10.1142/9789814374552_0008
DO - 10.1142/9789814374552_0008
M3 - Conference contribution
SN - 9814374512
SN - 9789814374514
T3 - 12th Marcel Grossmann Meeting on Recent Dev. in Theoretical and Experimental General Relativity, Astrophysics and Relativistic Field Theories - Proc. of the MG 2009 Meeting on General Relativity
SP - 132
EP - 189
BT - 12th Marcel Grossmann Meeting on Recent Dev. in Theoretical and Experimental General Relativity, Astrophysics and Relativistic Field Theories - Proc. of the MG 2009 Meeting on General Relativity
PB - World Scientific Publishing Co. Pte Ltd
T2 - 12th Marcel Grossmann Meeting on Recent Developments in Theoretical and Experimental General Relativity, Astrophysics and Relativistic Field Theories, MG 2009
Y2 - 12 July 2009 through 18 July 2009
ER -