The red-shift effect and radiation decay on black hole spacetimes

Communications on Pure and Applied Mathematics

Volumn 62, Issue 7, 2009, Pages 859-919

  Dafermos, Mihalis ^a   Rodnianski, Igor ^b  

^a UNIVERSITY OF CAMBRIDGE   (United Kingdom)

^b PRINCETON UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 68049137433     PISSN: 00103640     EISSN: 00103640     Source Type: Journal    
DOI: 10.1002/cpa.20281     Document Type: Article

References (27)

1. Blue, P.; Soffer, A. Semilinear wave equations on the Schwarzschild manifold. I. Local decay estimates. Adv. Differential Equations 8 (2003) no. 5, 595-614.
2. Blue, P.; Soffer, A. Errata for "Global existence and scattering for the nonlinear Schrodinger equation on Schwarzschild manifolds," "Semilinear wave equations on the Schwarzschild manifold I: Local decay estimates," and "The wave equation on the Schwarzschild metric II: Local decay for the spin 2 Regge Wheeler equation." arXiv: gr-qc/0608073, 2006.
3. Blue, P.; Sterbenz, J. Uniform decay of local energy and the semi-linear wave equation on Schwarzchild space. Comm. Math. Phys. 268 (2006), no. 2, 481-504.
4. Christodoulou, D. Self-gravitating relativistic fluids: a two-phase model. Arch. Rational Mech. Anal. 130 (1995), no. 4, 343-400.
5. Christodoulou, D. On the global initial value problem and the issue of singularities. Classical Quantum Gravity 16 (1999), no. 12A, A23-A35.
6. Christodoulou, D. The action principle and partial differential equations. Annals of Mathematics Studies, 146. Princeton University Press, Princeton, N.J., 2000.
7. Christodoulou, D.; Klainerman, S. The global nonlinear stability of the Minkowski space. Princeton Mathematical Series, 41. Princeton University Press, Princeton, N.J., 1993.
8. Dafermos, M. The interior of charged black holes and the problem of uniqueness in general relativity. Comm. Pure Appl. Math. 58 (2005), no. 4, 445-504.
9. Dafermos, M.; Rodnianski, I. A proof of Price's law for the collapse of a self-gravitating scalar field. Invent. Math. 162 (2005), no. 2, 381-457.
10. Dafermos, M.; Rodnianski, I. Small amplitude non-linear waves on a black hole background. J. Math. Pures Appl. 84 (2005), no. 9, 1147-1172.
11. Einstein, A. On a stationary system with spherical symmetry consisting of many gravitating masses. Ann. of Math. (2) 40 (1939), 922-936.
12. Finster, F.; Kamran, N.; Smoller, J.; Yau, S.-T. Decay of solutions of the wave equation in the Kerr geometry. Comm. Math. Phys. 264 (2006), no. 2, 465-503.
13. Gundlach, C.; Price, R. H.; Pullin, J. Late-time behavior of stellar collapse and explosions. I. Linearized perturbations. Phys. Rev. D 49 (1994), no. 2, 883-889.
14. Hawking, S.W.; Ellis, G. F. R. The large scale structure of space-time. Cambridge Monographs on Mathematical Physics, 1. Cambridge University Press, London-New York, 1973.
15. Hilbert, D. Die Grundlagen der Physik (Zweite Mitteilung). Nachrichten von der Königliche Gesellschaft der Wissenschaften zu Göttingen. Mathematische-Physikalische Klasse, 53-76. English translation: The foundations of physics (second communication). The genesis of general relativity. Vol. 4. Gravitation in the twilight of classical physics: The promise of mathematics, 1017-1038. Edited by J. Renn and M. Schemmel. Springer, Dordrecht, 2007.
16. Kay, B.;Wald, R. Linear stability of Schwarzschild under perturbations which are nonvanishing on the bifurcation 2-sphere. Classical Quantum Gravity 4 (1987), no. 4, 893-898.
17. Klainerman, S. Uniform decay estimates and the Lorentz invariance of the classical wave equation. Comm. Pure Appl. Math. 38 (1985), no. 3, 321-332.
18. Kruskal, M. Maximal extension of Schwarzschild metric. Phys. Rev. (2) 119 (1960), 1743-1745.
19. Łaba, I.; Soffer, A. Global existence and scattering for the nonlinear Schrödinger equation on Schwarzschild manifolds. Helv. Phys. Acta 72 (1999), no. 4, 274-294.
20. Lemaître, G. L'Univers en expansion. Ann. Soc. Sci. Bruxelles A 53 (1933), 51-85.
21. Machedon, M.; Stalker, J. Decay of solutions to the wave equation on a spherically symmetric background. Preprint, 2002.
22. Morawetz, C. S. Notes on time decay and scattering for some hyperbolic problems. Regional Conference Series in Applied Mathematics, 19. Society for Industrial and Applied Mathematics, Philadelphia, Pa., 1975.
23. Oppenheimer, J. R.; Snyder, H. On continued gravitational contraction. Phys. Rev. 56 (1939), no. 5, 455-459.
24. Price, R. H. Nonspherical perturbations of relativistic gravitational collapse. I. Scalar and gravitational perturbations. Phys. Rev. D (3) 5 (1972), 2419-2438.
25. Schwarzschild, K. Über das Gravitationsfeld eines Massenpunktes nach der Einsteinschen Theorie. Sitzungsberichte der Königlich Preussischen Akademie der Wissenschaften 1 (1916), 189-196.
26. Synge, J. L. Gravitational field of a particle. Proc. Roy. Irish Acad. 53 (1950), 83-114.
27. Twainy, F. The time decay of solutions to the scalar wave equation in Schwarzschild background. Doctoral dissertation, University of California, San Diego, 1989.