Linear stability of black holes [d'après M. Dafermos et I. Rodnianski]

Klainerman, Sergiu

Séminaire Bourbaki, volume 2009/2010, exposés 1012-1026, Astérisque, no. 339 (2011), Exposé no. 1015, 45 p.

[1] S. Alexakis, A. D. Ionescu & S. Klainerman - "Uniqueness of smooth stationary black holes in vacuum: small perturbations of the Kerr spaces", Comm. Math. Phys. 299 (2010), p. 89-127. | DOI | MR | Zbl

[2] S. Alexakis, A. D. Ionescu & S. Klainerman, "Hawking's local rigidity theorem without analyticity", preprint arXiv:0902.1173. | DOI | MR | Zbl

[3] S. Alinhac - "Energy multipliers for perturbations of the Schwarzschild metric", Comm. Math. Phys. 288 (2009), p. 199-224. | DOI | MR | Zbl

[4] L. Andersson & P. Blue - "Hidden symmetries and decay for the wave equation on the Kerr spacetime", preprint arXiv:0908.2265. | DOI | MR

[5] L. Bieri - "An extension of the stability theorem of the Minkowski space in general relativity", Ph.D. Thesis, ETH, Zürich, 2007.

[6] P. Blue & P. Soffer - "Semilinear wave equations on the schwarzschild manifold. I. Local decay estimates", preprint arXiv:gr-qc/0310091. | MR | Zbl

[7] P. Blue & J. Sterbenz - "Uniform decay of local energy and the semi-linear wave equation on Schwarzschild space", Comm. Math. Phys. 268 (2006), p. 481-504. | DOI | MR | Zbl

[8] B. Carter - "Hamilton-Jacobi and Schrödinger separable solutions of Einstein's equations", Comm. Math. Phys. 10 (1968), p. 280-310. | DOI | MR | Zbl

[9] S. Chandrasekhar - The mathematical theory of black holes, International Series of Monographs on Physics, vol. 69, The Clarendon Press, Oxford Univ. Press, 1983. | MR | Zbl

[10] Y. Choquet-Bruhat & R. Geroch - "Global aspects of the Cauchy problem in general relativity", Comm. Math. Phys. 14 (1969), p. 329-335. | DOI | MR | Zbl

[11] D. Christodoulou - The formation of black holes in general relativity, EMS Monographs in Math., European Mathematical Society (EMS), Zürich, 2009. | MR | Zbl

[12] D. Christodoulou & S. Klainerman - The global nonlinear stability of the Minkowski space, Princeton Math. Series, vol. 41, Princeton Univ. Press, 1993. | MR | Zbl

[13] P. T. Chruściel - "On completeness of orbits of Killing vector fields", Classical Quantum Gravity 10 (1993), p. 2091-2101. | DOI | MR | Zbl

[14] P. T. Chruściel & J. L. Costa - "On uniqueness of stationary vacuum black holes", Astérisque 321 (2008), p. 195-265. | Numdam | MR | Zbl

[15] P. T. Chruściel & R. M. Wald - "Maximal hypersurfaces in stationary asymptotically flat spacetimes", Comm. Math. Phys. 163 (1994), p. 561-604. | DOI | MR | Zbl

[16] M. Dafermos & I. Rodnianski - "The red-shift effect and radiation decay on black hole spacetimes", Comm. Pure Appl. Math. 62 (2009), p. 859-919. | DOI | MR | Zbl

[17] M. Dafermos & I. Rodnianski, "Lectures on black holes and linear waves", preprint arXiv:0811.0354. | MR

[18] M. Dafermos & I. Rodnianski, "A new physical space approach to decay for the wave equation with application to black hole spacetimes", preprint arXiv:0910.4957. | DOI | MR | Zbl

[19] M. Dafermos & I. Rodnianski, "A note on energy currents and decay for the wave equation on a Schwarzschild background", preprint arXiv:0710.017.

[20] M. Dafermos & I. Rodnianski, "A proof of uniform boundedness of solutions to wave equations on slowly rotating Kerr backgrounds", preprint arXiv:0805.4309. | DOI | MR | Zbl

[21] R. Donninger, W. Schlag & A. Soffer - "A proof of Price's law on Schwarzschild black hole manifolds for all angular momenta", preprint arXiv:gr-qc/0908.4292. | DOI | MR | Zbl

[22] F. Finster, N. Kamran, J. Smoller & S.-T. Yau - "Decay of solutions of the wave equation in the Kerr geometry", Comm. Math. Phys. 264 (2006), p. 465-503. | DOI | MR | Zbl

[23] Y. Fourès-Bruhat - "Théorème d'existence pour certains systèmes d'équations aux dérivées partielles non linéaires", Acta Math. 88 (1952), p. 141-225. | DOI | MR | Zbl

[24] S. W. Hawking & G. F. R. Ellis - The large scale structure of space-time, Cambridge Monographs on Math. Physics, vol. 1, Cambridge Univ. Press, 1973. | MR | Zbl

[25] T. J. R. Hughes, T. Kato & J. E. Marsden - "Well-posed quasi-linear second-order hyperbolic systems with applications to nonlinear elastodynamics and general relativity", Arch. Rational Mech. Anal. 63 (1976), p. 273-294. | DOI | MR | Zbl

[26] A. D. Ionescu & S. Klainerman - "On the uniqueness of smooth, stationary black holes in vacuum", Invent. Math. 175 (2009), p. 35-102. | DOI | MR | Zbl

[27] B. S. Kay & R. M. Wald - "Linear stability of Schwarzschild under perturbations which are nonvanishing on the bifurcation $2$-sphere", Classical Quantum Gravity 4 (1987), p. 893-898. | DOI | MR | Zbl

[28] S. Klainerman - "Uniform decay estimates and the Lorentz invariance of the classical wave equation", Comm. Pure Appl. Math. 38 (1985), p. 321-332. | DOI | MR | Zbl

[29] S. Klainerman, "The null condition and global existence to nonlinear wave equations", in Nonlinear systems of partial differential equations in applied mathematics, Part 1 (Santa Fe, N.M., 1984), Lectures in Appl. Math., vol. 23, Amer. Math. Soc., 1986, p. 293-326. | MR | Zbl

[30] S. Klainerman & F. Nicolò - The evolution problem in general relativity, Progress in Math. Physics, vol. 25, Birkhäuser, 2003. | MR | Zbl

[31] J. Kronthaler - "The Cauchy problem for the wave equation in the Schwarzschild geometry", J. Math. Phys. 47 (2006), 042501, 29. | DOI | MR | Zbl

[32] H. Lindblad & I. Rodnianski - "Global existence for the Einstein vacuum equations in wave coordinates", Comm. Math. Phys. 256 (2005), p. 43-110. | DOI | MR | Zbl

[33] J. Luk - "Improved decay for solutions to the linear wave equation on a Schwarzschild black hole", preprint arXiv:0906.5588. | MR | Zbl

[34] M. Machedon & J. Stalker - "Decay of solutions to the wave equation on a spherically symmetric background", preprint.

[35] J. Marzuola, J. Metcalfe, D. Tataru & M. Tohaneanu - "Strichartz estimates on Schwarzschild black hole backgrounds", Comm. Math. Phys. 293 (2010), p. 37-83. | DOI | MR | Zbl

[36] R. Penrose - "Gravitational collapse: the role of general relativity", Nuovo Cimento 1 (1969), p. 252-276. | MR | Zbl

[37] R. Penrose, Singularities and time asymmetry in general relativity - an Einstein Centenary survey, Cambridge Univ. Press, 1979.

[38] W. Press & S. Teukolsky - "Perturbations of a rotating black hole. II. Dynamical stability of the Kerr metric", Astrophys. J. 185 (1973), p. 649-673. | DOI

[39] R. H. Price - "Nonspherical perturbations of relativistic gravitational collapse. I. Scalar and gravitational perturbations", Phys. Rev. D 5 (1972), p. 2419-2438. | MR

[40] T. Regge & J. A. Wheeler - "Stability of a Schwarzschild singularity", Phys. Rev. 108 (1957), p. 1063-1069. | DOI | MR | Zbl

[41] A. A. Starobinsky - "Amplification of waves during reflection from a rotating black hole", Sov. Phys. JETP 37 (1973), p. 28-32.

[42] D. Tataru - "Local decay of waves on asymptotically flat stationary spacetimes", preprint arXiv:0910.5290. | Zbl

[43] D. Tataru & M. Tohaneanu - "Local energy estimate on Kerr Black hole backgrounds", preprint arXiv:0810.5766. | DOI | MR | Zbl

[44] Y. B. Zel'Dovich - "Amplification of cylindrical electromagnetic waves from a rotating body", Sov. Phys. JETP 35 (1972), p. 1085-1087.

[45] F. J. Zerilli - "Gravitational field of a particle falling in a Schwarzschild geometry analyzed in tensor harmonics", Phys. Rev. D 2 (1970), p. 2141-2160. | MR | Zbl