Decay of a linear scalar field on Schwarzschild space-time

 Access to full text

 Full (PDF)

1. P. Blue and J. Sterbenz Uniform decay of local energy and the semi-linear wave equation on Schwarzchild space, preprint MR2259204
2. D. Christodoulou The instability of naked singularities in the gravitational collapse of a scalar field, Ann. Math. 140 (1999), 183–217 Zbl1126.83305MR1680551
3. D. Christodoulou and S. Klainerman The global nonlinear stability of the Minkowski space Princeton University Press, 1993 Zbl0827.53055MR1316662
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 Zbl1071.83037MR2119866
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 Zbl1088.83008
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 Zbl0618.35088MR788801
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 $2$-sphere Classical Quantum Gravity 4 (1987), no. 4, 893–898 Zbl0647.53065MR895907
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 Zbl0635.35059MR784477
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 Zbl0303.35002MR492919
14. E. Poisson and W. Israel Inner-horizon instability and mass inflation in black holes, Phys. Rev. Lett. 63 (1989), 1663–1666 MR1018317
15. R. Price Nonspherical perturbations of relativistic gravitational collapse. I. Scalar and gravitational perturbations Phys. Rev. D (3) 5 (1972), 2419-2438 MR376103
16. F. Finster, N. Kamran, J. Smoller, S. T. Yau Decay of solutions of the wave equation in Kerr geometry, preprint Zbl1194.83014MR2215614
17. A. Sá Barreto and M. Zworski Distribution of resonances for spherical black holes, Math. Res. Lett. 4 (1997), 103–121 Zbl0883.35120MR1432814
18. F. Twainy The Time Decay of Solutions to the Scalar Wave Equation in Schwarzschild Background, Thesis, University of California, San Diego, 1989