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We establish the full global non-linear stability of the Kerr-de Sitter family of black holes, as solutions of the initial value problem for the Einstein vacuum equations with positive cosmological constant, for small angular momenta, and without any symmetry assumptions on the initial data.
L’intégration des équations de la gravitation relativiste et le probleme des n corps
André Lichnerowicz · 1944
Earlier work this paper cites.
Théorème d’existence pour certains systèmes d’équations aux dérivées partielles non linéaires
Yvonne Choquet-Bruhat · 1952
Earlier work this paper cites.
Stability of a Schwarzschild Singularity
Tullio Regge and John A. Wheeler · 1957
Earlier work this paper cites.
An Approach to Gravitational Radiation by a Method of Spin Coefficients
Ezra Newman and Roger Penrose · 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.
Hamilton–Jacobi and Schrödinger separable solutions of Einstein’s equations
Brandon Carter · 1968
Earlier work this paper cites.
Global aspects of the Cauchy problem in general relativity
Yvonne Choquet-Bruhat and Robert Geroch · 1969
Earlier work this paper cites.
Stability of the Schwarzschild Metric
C. V. Vishveshwara · 1970
Earlier work this paper cites.
Effective Potential for Even-Parity Regge–Wheeler Gravitational Perturbation Equations
Frank J. Zerilli · 1970
Earlier work this paper cites.
An operator generalization of the logarithmic residue theorem and Rouché’s theorem
Israel C. Gohberg and Efim I. Sigal · 1971
Earlier work this paper cites.
Radiation fields in the Schwarzschild background
James M. Bardeen and William H. Press · 1973
Earlier work this paper cites.
Perturbations of a rotating black hole. I. Fundamental equations for gravitational, electromagnetic, and neutrino-field perturbations
Saul A. Teukolsky · 1973
Earlier work this paper cites.
Conformally invariant orthogonal decomposition of symmetric tensors on Riemannian manifolds and the initial-value problem of general relativity
James W. York Jr · 1973
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Gravitational perturbations of spherically symmetric systems. I. The exterior problem
Vincent Moncrief · 1974
Earlier work this paper cites.
Invariant manifolds
Morris W. Hirsch, Michael Shub, and Charles C. Pugh · 1977
Earlier work this paper cites.
Note on the stability of the Schwarzschild metric
Robert M. Wald · 1979
Earlier work this paper cites.
Gauge-invariant coupled gravitational, acoustical, and electromagnetic modes on most general spherical space-times
Ulrich H. Gerlach and Uday K. Sengupta · 1980
Earlier work this paper cites.
Existence of metrics with prescribed Ricci curvature: local theory
Dennis M. DeTurck · 1981
Earlier work this paper cites.
Transformation of boundary problems
Richard B. Melrose · 1981
Earlier work this paper cites.
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Nils Dencker · 1982
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The inverse function theorem of Nash and Moser
Richard S. Hamilton · 1982
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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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Uniform decay estimates and the Lorentz invariance of the classical wave equation
Sergiu Klainerman · 1985
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Global solutions of nonlinear hyperbolic equations for small initial data
Demetrios Christodoulou · 1986
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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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The null condition and global existence to nonlinear wave equations
Sergiu Klainerman · 1986
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Atsushi Higuchi · 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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Rafe R. Mazzeo and Richard B. Melrose · 1987
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A simple Nash–Moser implicit function theorem
Xavier Saint-Raymond · 1989
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Mode stability of the Kerr black hole
Bernard F. Whiting · 1989
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Alan D. Rendall · 1990
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Alain Bachelot · 1991
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C. Robin Graham and John M. Lee · 1991
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The global nonlinear stability of the Minkowski space
Demetrios Christodoulou and Sergiu Klainerman · 1993
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The Atiyah–Patodi–Singer index theorem
Richard B. Melrose · 1993
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Richard B. Melrose · 1994
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Richard B. Melrose · 1995
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Michael E. Taylor · 1996
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Antônio Sá Barreto and Maciej Zworski · 1997
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Adam G. Riess et al · 1998
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Kostas D. Kokkotas and Bernd G. Schmidt · 1999
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Rafe R. Mazzeo and Richard B. Melrose · 1999
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Measurements of Ω \Omega and Λ \Lambda from 42 High-Redshift Supernovae
Saul Perlmutter et al · 1999
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Justin Corvino · 2000
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Asymptotic properties of the electromagnetic field in the external Schwarzschild spacetime
Walter Inglese and Francesco Nicolò · 2000
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Hideo Kodama, Akihiro Ishibashi, and Osamu Seto · 2000
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Future Global in Time Einsteinian Spacetimes with U ( 1 ) {U}(1) Isometry Group
Yvonne Choquet-Bruhat and Vincent Moncrief · 2001
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Xiaodong Wang · 2001
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Subrahmanyan Chandrasekhar · 2002
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Piotr T. Chruściel and Erwann Delay · 2003
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Piotr T. Chrusciel and Marc Herzlich · 2003
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Mihalis Dafermos · 2003
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Felix Finster, Niky Kamran, Joel Smoller, and Shing-Tung Yau · 2003
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Maciej Zworski · 2012
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Strichartz estimates on asymptotically de Sitter spaces
Dean Baskin · 2013
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Julien Cortier · 2013
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Mihalis Dafermos, Gustav Holzegel, and Igor Rodnianski · 2013
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Semyon Dyatlov and Maciej Zworski · 2013
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Jonathan Luk · 2013
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Stability of higher-dimensional Schwarzschild black holes
Akihiro Ishibashi and Hideo Kodama · 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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The Einstein Equations and the Large Scale Behavior of Gravitational Fields: 50 Years of the Cauchy Problem in General Relativity
Robert Bartnik and Jim Isenberg · 2004
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Bennett Chow and Dan Knopf · 2004
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Xiao Zhang · 2004
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Michael T. Anderson · 2005
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Jared Speck · 2013
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Local decay of waves on asymptotically flat stationary space-times
Daniel Tataru · 2013
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Microlocal analysis of asymptotically hyperbolic and Kerr–de Sitter spaces (with an appendix by Semyon Dyatlov)
András Vasy · 2013
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Rigidity of stationary black holes with small angular momentum on the horizon
Spyros Alexakis, Alexandru D. Ionescu, and Sergiu Klainerman · 2014
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Black holes without spacelike singularities
Mihalis Dafermos · 2014
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Non-trapping estimates near normally hyperbolic trapping
Peter Hintz and András Vasy · 2014
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Analytic continuation and semiclassical resolvent estimates on asymptotically hyperbolic spaces
Richard Melrose, Antônio Sá Barreto, and András Vasy · 2014
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Asymptotics of solutions of the wave equation on de Sitter–Schwarzschild space
Richard B. Melrose, Antônio Sá Barreto, and András Vasy · 2014
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The global stability of the Minkowski spacetime solution to the Einstein-nonlinear system in wave coordinates
Jared Speck · 2014
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Propagation phenomena
András Vasy · 2014
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Hidden symmetries and decay for the wave equation on the Kerr spacetime
Lars Andersson and Pieter Blue · 2015
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Uniform energy bound and asymptotics for the Maxwell field on a slowly rotating Kerr black hole exterior
Lars Andersson and Pieter Blue · 2015
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Asymptotics of radiation fields in asymptotically Minkowski space
Dean Baskin, András Vasy, and Jared Wunsch · 2015
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On the global uniqueness for the Einstein–Maxwell–scalar field system with a cosmological constant: I. Well posedness and breakdown criterion
João L. Costa, Pedro M. Girão, José Natário, and Jorge Drumond Silva · 2015
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On the global uniqueness for the Einstein–Maxwell–scalar field system with a cosmological constant. Part 2. Structure of the solutions and stability of the Cauchy horizon
João L. Costa, Pedro M. Girão, José Natário, and Jorge Drumond Silva · 2015
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Diffraction from conormal singularities
Maarten de Hoop, Gunther Uhlmann, and András Vasy · 2015
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Asymptotics of Linear Waves and Resonances with Applications to Black Holes
Semyon Dyatlov · 2015
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Resonance projectors and asymptotics for r r -normally hyperbolic trapped sets
Semyon Dyatlov · 2015
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Global analysis of linear and nonlinear wave equations on cosmological spacetimes
Peter Hintz · 2015
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Semilinear wave equations on asymptotically de Sitter, Kerr–de Sitter and Minkowski spacetimes
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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The global nonlinear stability of Minkowski space for self-gravitating massive fields
Philippe G. LeFloch and Yue Ma · 2015
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Global results for linear waves on expanding Kerr and Schwarzschild de Sitter cosmologies
Volker Schlue · 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
Claude M. Warnick · 2015
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Asymptotics of scalar waves on long-range asymptotically Minkowski spaces
Dean Baskin, András Vasy, and Jared Wunsch · 2016
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Conserved quantities on asymptotically hyperbolic initial data sets
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Decay for solutions of the wave equation on Kerr exterior spacetimes III: The full subextremal case | a | < M |a|<M
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Time-Translation Invariance of Scattering Maps and Blue-Shift Instabilities on Kerr Black Hole Spacetimes
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Spectral gaps for normally hyperbolic trapping
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Global well-posedness of quasilinear wave equations on asymptotically de Sitter spaces
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