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We prove Price's law with an explicit leading order term for solutions $\phi(t,x)$ of the scalar wave equation on a class of stationary asymptotically flat $(3+1)$-dimensional spacetimes including subextremal Kerr black holes.
Über das Gravitationsfeld eines Massenpunktes nach der Einsteinschen Theorie
Karl Schwarzschild · 1916
Earlier work this paper cites.
On the radiation field of pulse solutions of the wave equation
F. Gerard Friedlander · 1962
Earlier work this paper cites.
Gravitational field of a spinning mass as an example of algebraically special metrics
Roy P. Kerr · 1963
Earlier work this paper cites.
Fourier integral operators. II
Johannes J. Duistermaat and Lars Hörmander · 1972
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On the modes of decay for the wave equation in the exterior of a reflecting body
Cathleen Synge Morawetz · 1972
Earlier work this paper cites.
Nonspherical perturbations of relativistic gravitational collapse. I. Scalar and gravitational perturbations
Richard H. Price · 1972
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Nonspherical perturbations of relativistic gravitational collapse. II. Integer-spin, zero-rest-mass fields
Richard H Price · 1972
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Rotating black holes: Separable wave equations for gravitational and electromagnetic perturbations
Saul A. Teukolsky · 1972
Earlier work this paper cites.
Perturbations of a rotating black hole. II. Dynamical stability of the Kerr metric
William H. Press and Saul A. Teukolsky · 1973
Earlier work this paper cites.
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Arne Jensen and Tosio Kato · 1979
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Robert M. Wald · 1979
Earlier work this paper cites.
Global existence for nonlinear wave equations
Sergiu Klainerman · 1980
Earlier work this paper cites.
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Demetrios Christodoulou · 1986
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Edward W. Leaver · 1986
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Bernard S. Kay and Robert M. Wald · 1987
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Bernard F. Whiting · 1989
Earlier work this paper cites.
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Demetrios Christodoulou and Sergiu Klainerman · 1993
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Richard B. Melrose · 1993
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Carsten Gundlach, Richard H. Price, and Jorge Pullin · 1994
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Roberto Gómez, Jeffrey Winicour, and Bernd Schmidt · 1994
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Richard B. Melrose · 1994
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Andrew Hassell and András Vasy · 2001
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Pieter Blue and Avi Soffer · 2003
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Richard H. Price and Lior M. Burko · 2004
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Pieter Blue and Avi Soffer · 2005
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Mihalis Dafermos and Igor Rodnianski · 2005
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Decay of Solutions of the Wave Equation in the Kerr Geometry
Felix Finster, Niky Kamran, Joel Smoller, and Shing-Tung Yau · 2006
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Lars Hörmander · 2007
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Pieter Blue · 2008
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Resolvent at low energy and Riesz transform for Schrödinger operators on asymptotically conic manifolds. I
Colin Guillarmou and Andrew Hassell · 2008
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Reinaldo J. Gleiser, Richard H. Price, and Jorge Pullin · 2008
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Mihalis Dafermos and Igor Rodnianski · 2009
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Resolvent at low energy and Riesz transform for Schrödinger operators on asymptotically conic manifolds. II
Colin Guillarmou and Andrew Hassell · 2009
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Jean-François Bony and Dietrich Häfner · 2010
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Mihalis Dafermos and Igor Rodnianski · 2010
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Hans Lindblad and Igor Rodnianski · 2010
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Peter Hintz · 2016
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Peter Hintz and András Vasy · 2016
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Instability results for the wave equation in the interior of Kerr black holes
Jonathan Luk and Jan Sbierski · 2016
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The r p r^{p} -Weighted Energy Method of Dafermos and Rodnianski in General Asymptotically Flat Spacetimes and Applications
Georgios Moschidis · 2016
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Resonances for asymptotically hyperbolic manifolds: Vasy’s method revisited
Maciej Zworski · 2016
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Lars Andersson, Siyuan Ma, Claudio Paganini, and Bernard F. Whiting · 2017
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Mathematical theory of scattering resonances
Semyon Dyatlov and Maciej Zworski · 2019
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Linear stability of slowly rotating Kerr black holes
Dietrich Häfner, Peter Hintz, and András Vasy · 2019
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The linear stability of the Schwarzschild spacetime in the harmonic gauge: even part
Pei-Ken Hung · 2019
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Geometric and Obstacle Scattering at Low Energy
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