Small-amplitude nonlinear waves on a black hole background

Journal des Mathematiques Pures et Appliquees

Volumn 84, Issue 9, 2005, Pages 1147-1172

  Dafermos, Mihalis ^a   Rodnianski, Igor ^b  

^a UNIVERSITY OF CAMBRIDGE   (United Kingdom)

^b PRINCETON UNIVERSITY   (United States)

Author keywords

Black hole; Non linear wave equation; Reissner Nordstr m; Schwarzschild

Indexed keywords

EID: 24044503074     PISSN: 00217824     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.matpur.2005.04.004     Document Type: Article

References (22)

1. A. Bachelot J.-P. Nicolas Equation non linéaire de Klein-Gordon dans des métriques de type Schwarzschild C. R. Acad. Sci. Paris Sér. I Math. 316 10 1993 1047-1050
2. P. Blue A. Soffer Semilinear wave equations on the Schwarzschild manifold I: Local decay estimates Adv. Differential Equations 8 2003 595-614
3. D. Catania V. Georgiev Blowup for the semilinear equation in Schwarzschild metric math-ph/0407001 Preprint, 2004
4. E.S.C. Ching P.T. Leung W.M. Suen K. Young Wave propagation in gravitational systems Phys. Rev. D 52 4 1995
5. D. Christodoulou The instability of naked singularities in the gravitational collapse of a scalar field Ann. of Math. 149 1 1999 183-217
6. M. Dafermos Spherically symmetric spacetimes with a trapped surface Class. Quantum Grav. 22 2005 2221-2232
7. M. Dafermos On naked singularities and the collapse of self-gravitating Higgs fields gr-qc/0403033 Preprint, 2004
8. M. Dafermos I. Rodnianski A proof of Price's law for the collapse of a self-gravitating scalar field gr-qc/0309115 Invent. Math., submitted for publication
9. C. Gundlach R.H. Price J. Pullin Late-time behavior of stellar collapse and explosions. I. Linearized perturbations Phys. Rev. D 49 1994 883-889
10. V. Georgiev H. Lindblad C. Sogge Weighted Strichartz estimates and global existence for semilinear wave equations Amer. J. Math. 119 1997 1291-1319
11. S.W. Hawking G.F.R. Ellis The Large Scale Structure of Space-Time Cambridge Monogr. Math. Phys. vol. 1 1973 Cambridge Univ. Press London-New York
12. T. Hertog G.T. Horowitz K. Maeda Generic cosmic censorship violation in anti de Sitter space Phys. Rev. Lett. 92 2004 131101
13. T. Hertog G.T. Horowitz K. Maeda Update on cosmic censorship violation in AdS gr-qc/0405050 Preprint, 2004
14. F. John Blow-up of solutions of nonlinear wave equation in three dimensions Manuscripta Math. 28 1979 235-265
15. P. Karageorgis, Existence and blow-up of small amplitude non-linear waves with sign-changing potential, J. Differential Equations, submitted for publication
16. B. Kay R. Wald Linear stability of Schwarzschild under perturbations which are nonvanishing on the bifurcation 2-sphere Class. Quantum Grav. 4 4 1987 893-989
17. M. Machedon, J. Stalker, Decay of solutions to the wave equation on a spherically symmetric background, Preprint
18. J.-P. Nicolas Nonlinear Klein-Gordon equation on Schwarschild-like metrics J. Math. Pures Appl. 74 1995 35-58
19. J.-P. Nicolas A nonlinear Klein-Gordon equation on Kerr metrics J. Math. Pures Appl. 81 2002 885-914
20. R.H. Price Nonspherical perturbations of relativistic gravitational collapse. I. Scalar and gravitational perturbations Phys. Rev. D (3) 5 1972 2419-2438
21. p for the critical value of p Proc. Roy. Soc. Edinburgh Sect. A 101 1985 31-44
22. F. Twainy, The time decay of solutions to the scalar wave equation in Schwarzschild background, Thesis, University of California, San Diego, 1989