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We prove the linear stability of slowly rotating Kerr black holes as solutions of the Einstein vacuum equation: linearized perturbations of a Kerr metric decay at an inverse polynomial rate to a linearized Kerr metric plus a pure gauge term.
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Yvonne Choquet-Bruhat · 1952
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Tullio Regge and John A. Wheeler · 1957
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An Approach to Gravitational Radiation by a Method of Spin Coefficients
Ezra Newman and Roger Penrose · 1962
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Gravitational field of a spinning mass as an example of algebraically special metrics
Roy P. Kerr · 1963
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Global aspects of the Cauchy problem in general relativity
Yvonne Choquet-Bruhat and Robert Geroch · 1969
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Stability of the Schwarzschild Metric
C. V. Vishveshwara · 1970
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Effective Potential for Even-Parity Regge–Wheeler Gravitational Perturbation Equations
Frank J. Zerilli · 1970
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Fourier integral operators. II
Johannes J. Duistermaat and Lars Hörmander · 1972
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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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James M. Bardeen and William H. Press · 1973
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A space-time calculus based on pairs of null directions
Robert Geroch, Alan Held, and Roger Penrose · 1973
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Perturbations of a rotating black hole. I. Fundamental equations for gravitational, electromagnetic, and neutrino-field perturbations
Saul A. Teukolsky · 1973
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Morris W. Hirsch, Charles C. Pugh, and Michael Shub · 1977
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Note on the stability of the Schwarzschild metric
Robert M. Wald · 1979
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Radiation fields and hyperbolic scattering theory
F. Gerard Friedlander · 1980
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Existence of metrics with prescribed Ricci curvature: local theory
Dennis M. DeTurck · 1981
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The mathematical theory of black holes
Subrahmanyan Chandrasekhar · 1983
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Parallel-tetrad on null geodesics in Kerr–Newman space-time
Jean-Alain Marck · 1983
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Cosmological Perturbation Theory
Hideo Kodama and Misao Sasaki · 1984
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On the hyperbolicity of Einstein’s and other gauge field equations
Helmut Friedrich · 1985
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On the existence of n n -geodesically complete or future complete solutions of Einstein’s field equations with smooth asymptotic structure
Helmut Friedrich · 1986
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Black holes in higher dimensional space-times
Robert C. Myers and Michael J. Perry · 1986
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Semiclassical resonances generated by a closed trajectory of hyperbolic type
Christian Gérard and Johannes Sjöstrand · 1987
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Linear stability of Schwarzschild under perturbations which are non-vanishing on the bifurcation 2-sphere
Bernard S. Kay and Robert M. Wald · 1987
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Mode stability of the Kerr black hole
Bernard F. Whiting · 1989
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C. Robin Graham and John M. Lee · 1991
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Rafe R. Mazzeo · 1991
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Demetrios Christodoulou and Sergiu Klainerman · 1993
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Richard B. Melrose · 1993
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Richard B. Melrose · 1994
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Geometric scattering theory
Richard B. Melrose · 1995
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Distribution of resonances for spherical black holes
Antônio Sá Barreto and Maciej Zworski · 1997
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Quasi-spherical light cones of the Kerr geometry
Frans Pretorius and Werner Israel · 1998
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Hideo Kodama, Akihiro Ishibashi, and Osamu Seto · 2000
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Semiclassical Estimates in Asymptotically Euclidean Scattering
András Vasy and Maciej Zworski · 2000
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The long-time dynamics of Dirac particles in the Kerr–Newman black hole geometry
Felix Finster, Niky Kamran, Joel Smoller, and Shing-Tung Yau · 2003
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A master equation for gravitational perturbations of maximally symmetric black holes in higher dimensions
Hideo Kodama and Akihiro Ishibashi · 2003
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Constraint damping in the Z4 formulation and harmonic gauge
Carsten Gundlach, Gioel Calabrese, Ian Hinder, and José M. Martín-García · 2005
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The analysis of linear partial differential operators. II
Lars Hörmander · 2005
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Evolution of Binary Black-Hole Spacetimes
Frans Pretorius · 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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Hans Christianson · 2007
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Mihalis Dafermos and Igor Rodnianski · 2007
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Lars Hörmander · 2007
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Jean-François Bony and Dietrich Häfner · 2008
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Pieter Blue · 2008
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Semyon Dyatlov · 2015
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Peter Hintz and András Vasy · 2015
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On the global stability of the wave-map equation in Kerr spaces with small angular momentum
Alexandru D. Ionescu and Sergiu Klainerman · 2015
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Quantitative mode stability for the wave equation on the Kerr spacetime
Yakov Shlapentokh-Rothman · 2015
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Local energy decay for Maxwell fields part I: Spherically symmetric black-hole backgrounds
Jacob Sterbenz and Daniel Tataru · 2015
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On quasinormal modes of asymptotically anti-de Sitter black holes
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Colin Guillarmou and Andrew Hassell · 2008
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Colin Guillarmou and Andrew Hassell · 2009
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Alexandru D. Ionescu and Sergiu Klainerman · 2009
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David C. Robinson · 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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Claude M. Warnick · 2015
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Mode stability on the real axis
Lars Andersson, Siyuan Ma, Claudio Paganini, and Bernard F. Whiting · 2016
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The linear stability of the Schwarzschild solution to gravitational perturbations
Mihalis Dafermos, Gustav Holzegel, and Igor Rodnianski · 2016
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Decay for solutions of the wave equation on Kerr exterior spacetimes III: The full subextremal case | a | < M |a|<M
Mihalis Dafermos, Igor Rodnianski, and Yakov Shlapentokh-Rothman · 2016
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Spectral gaps for normally hyperbolic trapping
Semyon Dyatlov · 2016
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Linear stability of the non-extreme Kerr black hole
Felix Finster and Joel Smoller · 2016
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Linear stability of Schwarzschild spacetime subject to axial perturbations
Pei-Ken Hung and Jordan Keller · 2016
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Global Analysis of Quasilinear Wave Equations on Asymptotically Kerr–de Sitter Spaces
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Resonances for asymptotically hyperbolic manifolds: Vasy’s method revisited
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Boundedness and decay for the Teukolsky equation on Kerr spacetimes I: the case | a | ≪ M |a|\ll{M}
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Elena Giorgi · 2017
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Peter Hintz · 2017
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Linear stability of Schwarzschild spacetime: decay of metric coefficients
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A global analysis proof of the stability of Minkowski space and the polyhomogeneity of the metric
Peter Hintz and András Vasy · 2017
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Decay of Solutions to the Maxwell Equations on Schwarzschild–de Sitter Spacetimes
Jordan Keller · 2017
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Global nonlinear stability of Schwarzschild spacetime under polarized perturbations
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Siyuan Ma · 2017
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Non-linear Stability of the Kerr–Newman–de Sitter Family of Charged Black Holes
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Normally hyperbolic trapping on asymptotically stationary spacetimes
Peter Hintz · 2018
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Uniqueness of Kerr–Newman–de Sitter Black Holes with Small Angular Momenta
Peter Hintz · 2018
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Linear stability of higher dimensional Schwarzschild spacetimes: decay of master quantities
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The linear stability of the Schwarzschild spacetime in the harmonic gauge: odd part
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Asymptotics for the wave equation on differential forms on Kerr–de Sitter space
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The global non-linear stability of the Kerr–de Sitter family of black holes
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