@article{SEDP_2005-2006____A11_0, author = {Rodnianski, Igor}, title = {Decay of a linear scalar field on {Schwarzschild} space-time}, journal = {S\'eminaire \'Equations aux d\'eriv\'ees partielles (Polytechnique) dit aussi "S\'eminaire Goulaouic-Schwartz"}, note = {talk:11}, pages = {1--13}, publisher = {Centre de math\'ematiques Laurent Schwartz, \'Ecole polytechnique}, year = {2005-2006}, language = {en}, url = {http://www.numdam.org/item/SEDP_2005-2006____A11_0/} }
TY - JOUR AU - Rodnianski, Igor TI - Decay of a linear scalar field on Schwarzschild space-time JO - Séminaire Équations aux dérivées partielles (Polytechnique) dit aussi "Séminaire Goulaouic-Schwartz" N1 - talk:11 PY - 2005-2006 SP - 1 EP - 13 PB - Centre de mathématiques Laurent Schwartz, École polytechnique UR - http://www.numdam.org/item/SEDP_2005-2006____A11_0/ LA - en ID - SEDP_2005-2006____A11_0 ER -
%0 Journal Article %A Rodnianski, Igor %T Decay of a linear scalar field on Schwarzschild space-time %J Séminaire Équations aux dérivées partielles (Polytechnique) dit aussi "Séminaire Goulaouic-Schwartz" %Z talk:11 %D 2005-2006 %P 1-13 %I Centre de mathématiques Laurent Schwartz, École polytechnique %U http://www.numdam.org/item/SEDP_2005-2006____A11_0/ %G en %F SEDP_2005-2006____A11_0
Rodnianski, Igor. Decay of a linear scalar field on Schwarzschild space-time. Séminaire Équations aux dérivées partielles (Polytechnique) dit aussi "Séminaire Goulaouic-Schwartz" (2005-2006), Talk no. 11, 13 p. http://www.numdam.org/item/SEDP_2005-2006____A11_0/
[1] P. Blue and J. Sterbenz Uniform decay of local energy and the semi-linear wave equation on Schwarzchild space, preprint | MR
[2] D. Christodoulou The instability of naked singularities in the gravitational collapse of a scalar field, Ann. Math. 140 (1999), 183–217 | MR | Zbl
[3] D. Christodoulou and S. Klainerman The global nonlinear stability of the Minkowski space Princeton University Press, 1993 | MR | Zbl
[4] M. Dafermos The interior of charged black holes and the problem of uniqueness in general relativity Comm. Pure Appl. Math. 58 (2005), 0445–0504 | MR | Zbl
[5] M. Dafermos and I. Rodnianski A proof of Price’s law for the collapse of a self-gravitating scalar field Invent. Math. 162 (2005), 381–457 | Zbl
[6] M. Dafermos and I. Rodnianski The red-shift effect and radiation decay on black hole spacetimes, submitted
[7] J. Dimock Scattering for the wave equation on the Schwarzschild Metric, Gen. Rel. Grav. 17 (1985), 353–369 | MR | Zbl
[8] C. Gundlach, R. H. Price, and J. Pullin Late-time behavior of stellar collapse and explosions. I. Linearized perturbations Phys. Rev. D 49 (1994), 883–889
[9] B. Kay and R. Wald Linear stability of Schwarzschild under perturbations which are nonvanishing on the bifurcation -sphere Classical Quantum Gravity 4 (1987), no. 4, 893–898 | MR | Zbl
[10] H. Lindblad and I. Rodnianski The global stability of the Minkowski space-time in harmonic gauge, to appear in Ann. Math.
[11] S. Klainerman Uniform decay estimates and the Lorentz invariance of the classical wave equations Comm. Pure Appl. Math. 38 (1985), 321-332 | MR | Zbl
[12] M. Machedon and J. Stalker Decay of solutions to the wave equation on a spherically symmetric background, preprint
[13] C. Morawetz Notes on the decay and scattering for some hyperbolic problems CBMS-NSF Regional Conference Series in Applied Mathematics 19, 1975 | MR | Zbl
[14] E. Poisson and W. Israel Inner-horizon instability and mass inflation in black holes, Phys. Rev. Lett. 63 (1989), 1663–1666 | MR
[15] R. Price Nonspherical perturbations of relativistic gravitational collapse. I. Scalar and gravitational perturbations Phys. Rev. D (3) 5 (1972), 2419-2438 | MR
[16] F. Finster, N. Kamran, J. Smoller, S. T. Yau Decay of solutions of the wave equation in Kerr geometry, preprint | MR
[17] A. Sá Barreto and M. Zworski Distribution of resonances for spherical black holes, Math. Res. Lett. 4 (1997), 103–121 | MR | Zbl
[18] F. Twainy The Time Decay of Solutions to the Scalar Wave Equation in Schwarzschild Background, Thesis, University of California, San Diego, 1989