Decay for solutions of the wave equation on Kerr exterior spacetimes III: The full subextremal case |a| < M

By Mihalis Dafermos, Igor Rodnianski, Yakov Shlapentokh-Rothman. 2014

250 citations recorded by the source corpus.

This paper concludes the series begun in [M. Dafermos and I. Rodnianski, Decay for solutions of the wave equation on Kerr exterior spacetimes I-II: the cases |a| << M or axisymmetry, 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 [M. Dafermos and I. Rodnianski, The black hole stability problem for linear scalar perturbations, in Proceedings of the 12th Marcel Grossmann Meeting on General Relativity, T. Damour et al (ed.), World Scientific, Singapore, 2011, pp. 132-189, arXiv:1010.5137]. Our proof appeals also to the quantitative mode-stability proven in [Y. Shlapentokh-Rothman, Quantitative Mode Stability for the Wave Equation on the Kerr Spacetime, arXiv:1302.6902, to appear, Ann. Henri Poincare], 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 notations so that it can be read independently of previous work.

Subfields: Mathematical Physics, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/c3033c26097004b9a9c4638abfdc2ce12007a115

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In Mathematical Physics

1. Lars-Erik Andersson
2. P. Hintz
3. Jacques Smulevici
4. P. Blue
5. Joseph Keir
6. András Vasy
7. Mihalis Dafermos
8. Igor Rodnianski

In Nuclear and High Energy Physics

1. Jacques Smulevici
2. P. Blue
3. P. Hintz
4. Joseph Keir
5. András Vasy
6. Lars-Erik Andersson
7. Hans Ringstrom

Citations in the corpus

• Slowly decaying waves on spherically symmetric spacetimes and ultracompact neutron stars (2014, background): “In [4], logarithmic decay was proved as an upper bound for Kerr-AdS, and so the results of [5] showed that in fact this decay estimate is sharp.”
• Small Data Solutions of the Vlasov-Poisson System and the Vector Field Method (2015, background): “3More recently, a mix of microlocal and vector field methods have also been successfully developped, in particular to handle complex geometries involving trapped trajectories, see for instance [12] for an application of these tools.”
• Hidden symmetries and decay for the wave equation on the Kerr spacetime (2009, background): “During the preparation of this paper, uniform energy and Morawetz estimates have been obtained for the full range |a| < M [21].”
• The global non-linear stability of the Kerr-de Sitter family of black holes (2016, methodology): “After pioneering work by Wald [143] and Kay–Wald [87], Dafermos, Rodnianski and Shlapentokh–Rothman [42], [44] recently proved polynomial decay for the scalar wave equation on all (exact) subextremal Kerr spacetimes; Tataru and Tohaneanu [131], [132] proved Price’s law, i.”