The formation of black holes in general relativity [after D. Christodoulou]
Séminaire Bourbaki volume 2011/2012 exposés 1043-1058, Astérisque, no. 352 (2013), Exposé no. 1051, 71 p.
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Dafermos, Mihalis. The formation of black holes in general relativity [after D. Christodoulou], dans Séminaire Bourbaki volume 2011/2012 exposés 1043-1058, Astérisque, no. 352 (2013), Exposé no. 1051, 71 p. http://archive.numdam.org/item/AST_2013__352__243_0/

[1] L. Bieri & N. Zipser - Extensions of the stability theorem of the Minkowski space in general relativity, AMS/IP Studies in Advanced Math., vol. 45, Amer. Math. Soc, 2009. | MR | Zbl

[2] 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

[3] D. Christodoulou - "Violation of cosmic censorship in the gravitational collapse of a dust cloud", Comm. Math. Phys. 93 (1984), no. 2, p. 171-195. | DOI | MR

[4] D. Christodoulou, "Nonlinear nature of gravitation and gravitational-wave experiments", Phys. Rev. Lett 67 (1991), no. 12, p. 1486-1489. | DOI | MR | Zbl

[5] D. Christodoulou, "Examples of naked singularity formation in the gravitational collapse of a scalar field", Ann. of Math. 140 (1994), no. 3, p. 607-653. | DOI | MR | Zbl

[6] D. Christodoulou, "The instability of naked singularities in the gravitational collapse of a scalar field", Ann. of Math. 149 (1999), no. 1, p. 183-217. | DOI | EuDML | MR | Zbl

[7] D. Christodoulou, "On the global initial value problem and the issue of singularities", Classical Quantum Gravity 16 (1999), no. 12A, p. A23-A35. | DOI | MR | Zbl

[8] D. Christodoulou, "The global initial value problem in general relativity", in 9th Marcel Grosmann Meeting (Rome 2000), World Sci. Publishing, 2002, p. 44-54. | Zbl

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

[10] D. Christodoulou, "Notes on the geometry of null hypersurfaces".

[11] D. Christodoulou, "Topics on black holes and gravitational waves", lectures held at ETH-Zürich, 2011.

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

[13] M. Dafermos & I. Rodnianski - "A new physical-space approach to decay for the wave equation with applications to black hole spacetimes", in XVIth International Congress on Mathematical Physics, World Sci. Publ., Hackensack, NJ, 2010, p. 421-432. | DOI | MR | Zbl

[14] M. Dafermos & I. Rodnianski, "Lectures on black holes and linear waves", to be published by Clay Mathematics Institute. | MR | Zbl

[15] T. De Donder - "La gravifique einsteinienne", Annales de l'Observatoire Royal de Belgique (1921). | JFM

[16] A. Einstein - "Über Gravitationswellen", Königlich Preussiche Akademie der Wissenschaften Berlin Sitzungberichte (1918), p. 154-167. | JFM

[17] 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

[18] H. Friedrich - "The asymptotic characteristic initial value problem for Einstein's vacuum field equations as an initial value problem for a first-order quasilinear symmetric hy", Proc. Roy. Soc. London Ser. A 378 (1981) , no. 1774, p. 401-421. | DOI | MR | Zbl

[19] K. Friedrichs & H. Lewy - "Über die Eindeutigkeit und das Abhängigkeits-gebiet der Lösungen beim Anfangswertproblem linearer hyperbolischer Differentialgleichungen", Math. Ann. 98 (1928) , no. 1, p. 192-204. | DOI | EuDML | JFM | MR

[20] H. Müller Zum Hagen - "Characteristic initial value problem for hyperbolic systems of second order differential equations", Ann. Inst. H. Poincaré Phys. Théor. 53 (1990), no. 2, p. 159-216. | EuDML | Numdam | MR | Zbl

[21] S. W. Hawking & G. F. R. Ellis - The large scale structure of space-time, Cambridge Univ. Press, 1973, Cambridge Monographs on Mathematical Physics, No. 1. | MR | Zbl

[22] D. Kennefick - "Controversies in the history of the radiation reaction problem in general relativity", in The expanding worlds of general relativity (Berlin, 1995), Einstein Stud., vol. 7, Birkhäuser, 1999, p. 207-234. | DOI | MR | Zbl

[23] S. Klainerman - "Uniform decay estimates and the Lorentz invariance of the classical wave equation", Comm. Pure Appl. Math. 38 (1985) , no. 3, p. 321-332. | DOI | MR | Zbl

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

[25] S. Klainerman & I. Rodnianski - "Rough solutions of the Einstein-vacuum equations", Ann. of Math. 161 (2005) , no. 3, p. 1143-1193. | DOI | MR | Zbl

[26] S. Klainerman, "On emerging scarred surfaces for the Einstein vacuum equations", Discrete Contin. Dyn. Syst. 28 (2010) , no. 3, p. 1007-1031. | DOI | MR | Zbl

[27] S. Klainerman, "On the formation of trapped surfaces", Acta Math. 208 (2012) , no. 2, p. 211-333. | DOI | MR | Zbl

[28] G. Lemaître - "L'univers en expansion", Publication du Laboratoire d'Astronomie et de Géodésie de l'Université de Louvain 9 (1932) , p. 171-205. | JFM | Zbl

[29] J. Leray - Hyperbolic differential equations, The Institute for Advanced Study, Princeton, N. J., 1953. | MR

[30] H. Lindblad & I. Rodnianski - "The global stability of Minkowski space-time in harmonic gauge", Ann. of Math. 171 (2010), no. 3, p. 1401-1477. | DOI | MR | Zbl

[31] J. Luk - "On the local existence for the characteristic initial value problem in general relativity", Int. Math. Res. Not. 2012 (2012), no. 20, p. 4625-4678. | DOI | MR | Zbl

[32] E. Newman & R. Penrose - "An approach to gravitational radiation by a method of spin coefficients", J. Mathematical Phys. 3 (1962) , p. 566-578. | DOI | MR | Zbl

[33] J. R. Oppenheimer & H. Snyder "On continued gravitational contraction", Phys. Rev. 56 (1939), p. 455-459. | DOI | Zbl

[34] R. Penrose - "Gravitational collapse and space-time singularities", Phys. Rev. Lett. 14 (1965), p. 57-59. | DOI | MR | Zbl

[35] F. A. E. Pirani - "Invariant formulation of gravitational radiation theory", Phys. Rev. 105 (1957), p. 1089-1099. | DOI | MR | Zbl

[36] F. Planchon & I. Rodnianski - "On uniqueness for the Cauchy problem in general relativity", preprint.

[37] M. Reiterer & E. Trubowitz - "Strongly focused gravitational waves", Comm. Math. Phys. 307 (2011), no. 2, p. 275-313. | DOI | MR | Zbl

[38] A. D. Rendall - "Reduction of the characteristic initial value problem to the Cauchy problem and its applications to the Einstein equations", Proc. Roy. Soc. London Ser. A 427 (1990), no. 1872, p. 221-239. | DOI | MR | Zbl

[39] J. Schauder - "Das Anfangswertproblem einer quasilinearen hyperbolischen Differentialgleichung zweiter Ordnung in beliebiger Anzahl yon unabhängigen Veränderlichen", Fundam. Math. 24 (1935). | DOI | EuDML | Zbl

[40] K. Stellmacher - "Zum Anfangswertproblem der Gravitationsgleichungen", Math. Ann. 115 (1938), no. 1, p. 136-152. | DOI | EuDML | JFM | MR

[41] K. S. Thorne - "Gravitational-wave bursts with memory: the Christodoulou effect", Phys. Rev. D 45 (1992), no. 2, p. 520-524. | DOI | MR

[42] R. M. Wald - General relativity, University of Chicago Press, 1984. | MR | Zbl

[43] P. Yu - "Dynamical formation of black holes due to the condensation of matter field", preprint arXiv: 1105.5898.