Sur quelques problèmes d’analyse globale en relativité générale

 Access to full text

 Full (PDF)

1. Andersson L., Blue P. Hidden symmetries and decay for the wave equation on the Kerr spacetime (2009). http://arxiv.org/abs/0908.2265. Zbl06514748
2. Andersson L., Blue P., Uniform energy bound and asymptotics for the Maxwell field on a slowly rotating Kerr black hole exterior. http://arxiv.org/abs/1310.2664. Zbl06575417
3. Aretakis S. Horizon Instability of Extremal Black Holes. http://arxiv.org/abs/1206.6598. Zbl1335.83013
4. Bachelot A. The Dirac System on the Anti-de-Sitter Universe. Commun. Math. Phys.283 (2008), 127–167. Zbl1153.83013MR2430631
5. Bizon P., Rostworowski A. On weakly turbulent instability of anti-de-Sitter space. Phys.Rev.Lett. 107 (2011), 031102, http://arxiv.org/abs/1104.3702. Zbl1328.83031
6. Blue P., Decay of the Maxwell field on the Schwarzschild manifold. http://arxiv.org/abs/0710.4102. Zbl1169.35057MR2475482
7. Bony, J.-F., Häfner, D. Decay and non-decay of the local energy for the wave equation in the De Sitter-Schwarzschild metric. Comm. Math. Phys.282 (2008), 697–719. Zbl1159.35007MR2426141
8. Choquet-Bruhat Y., General relativity and the Einstein equations. Oxford Mathematical Monographs. Oxford University Press, Oxford, 2009. Zbl1157.83002MR2473363
9. Foures-Bruhat Y., Théorèmes d’existence pour certains systèmes d’équations aux dérivées partielles non-linéaires, Acta Mathematica 88 (1952), 141–225. Zbl0049.19201MR53338
10. Christodoulou D., Klainerman S. The global nonlinear stability of the Minkowski space Princeton University Press, 1993 Zbl0827.53055MR1316662
11. Dafermos M., Rodnianski I., Decay for solutions of the wave equation on Kerr exterior spacetimes I-II : The cases $\left|a\right|\ll M$ or axisymmetry (2010). http://arxiv.org/abs/1010.5132. MR2730803
12. Dafermos M., Rodnianski I., The wave equation on Schwarzschild-de-Sitter spacetimes http://arxiv.org/abs/0709.2766. Zbl1211.83019
13. Dafermos M., Rodnianski I., A new physical-space approach to decay for the wave equation with applications to black hole spacetimes. XVI International Congress on Mathematical Physics, P. Exner (ed), World Scientific, London (2009). Zbl1211.83019MR2730803
14. Dafermos M., Rodnianski I., A proof of the uniform boundedness of solutions to the wave equation on slowly rotating Kerr backgrounds. Invent. Math. 185 (3) (2011), 467–559. http://arxiv.org/abs/0805.4309. Zbl1226.83029MR2827094
15. Dafermos M., Rodnianski I., Lectures on black holes and linear waves. Institut Mittag-Leffler Report no. 14, 2008/2009 (2008), http://arxiv.org/abs/0811.0354. MR3098640
16. Dafermos M., Holzegel G., Rodnianski I., A scattering theory construction of dynamical vacuum black holes. http://arxiv.org/abs/1306.5364. 
17. Dafermos M., Holzegel G., Rodnianski I., Linear Stability of the Schwarzschild Solution, présentation donnée par G. Holzegel lors de la conférence Initial Data and Evolution Problems in General Relativity, MSRI, Berkeley. 
18. Dafermos M., Rodnianski I., Shlapentokh-Rothman Y. Decay for solutions of the wave equation on Kerr exterior spacetimes III : The full subextremal case |a| < M. http://arxiv.org/abs/1402.7034. Zbl06589409
19. Dyatlov S. Asymptotic distribution of quasi-normal modes for Kerr-de-Sitter black holes (2011). Annales Henri Poincaré July 2012, Volume 13, Issue 5, pp 1101-1166 Zbl1246.83111MR2935116
20. Dyatlov S. Quasi-normal modes and exponential energy decay for the Kerr-de Sitter black hole. Comm. Math. Phys.306 (2011), 119–163. Zbl1223.83029MR2819421
21. Dyatlov S., Zworski M. Trapping of waves and null geodesics for rotating black holes. http://arxiv.org/abs/1305.4603. Zbl1278.81100
22. Friedrich H. The existence of $n$-geodesically complete or future complete solutions of Einstein’s field equations with smooth asymptotic structure Comm. Math. Phys. 107 (1986), no. 4, 587–609 Zbl0659.53056MR868737
23. Gannot O. Quasinormal modes for Schwarzschild-AdS black holes : exponential convergence to the real axis http://arxiv.org/abs/1212.1907. 
24. Holzegel G. Well-posedness for the massive wave equation on asymptotically anti-de-Sitter spacetimes. J. Hyperbolic Differ. Equ.9 (2012), 239–261. Zbl1250.83025MR2928108
25. Holzegel G. On the massive wave equation on slowly rotating Kerr-AdS spacetimes. Comm. Math. Phys.294 (2010), 169–197. Zbl1210.58023MR2575480
26. Holzegel G., Warnick C. Boundedness and growth for the massive wave equation on asymptotically anti-de-Sitter black holes (2012). Zbl1292.83033
27. Holzegel G., Smulevici J. Decay properties of Klein-Gordon fields on Kerr-AdS spacetimes. Communications on Pure and Applied Mathematics Volume 66, Issue 11, p. 1751-1802, November 2013. Zbl1277.83023MR3103910
28. Holzegel G., Smulevici J. Quasimodes and a Lower Bound on the Uniform Energy Decay Rate for Kerr-AdS Spacetimes. http://arxiv.org/abs/1303.5944. Zbl1300.83030
29. Ionescu A., Klainerman S., Szeftel J., On the reality of Black holes. Présentation donnée par S. Klainerman lors de la conférence Nonlinear Wave Equations and General Relativity Workshop, Oxford University. 
30. Ishibashi, A., Wald R. M. Dynamics in non-globally hyperbolic static spacetimes. III : anti-de Sitter spacetime. Class. Quant. Grav. 21 (2004), 2981–3014, http://arxiv.org/abs/hep-th/0402184. Zbl1064.83006MR2079784
31. Klainerman S., Rodnianski I., Szeftel J. Overview of the proof of the Bounded $L^2$ Curvature Conjecture. http://arxiv.org/abs/1204.1772. Zbl1330.53089MR2151111
32. Klainerman S., Rodnianski I., Szeftel J., The bounded $L^2$ curvature conjecture. http://arxiv.org/abs/1204.1767, 91 pp. Zbl1330.53089MR2151111
33. Lindblad H. and Rodnianski I., The global stability of Minkowski space-time in harmonic gauge, Ann. of Math. p 1401-1477 Volume 171 (2010), Issue 3 Zbl1192.53066MR2680391
34. Marzuola J., Metcalfe J., Tataru D., Tohaneanu M., Strichartz Estimates on Schwarzschild Black Hole Backgrounds. Comm. Math. Phys.293 (2010). http://arxiv.org/abs/0802.3942. Zbl1202.35327MR2563798
35. Metcalfe J., Tataru D., Tohaneanu M., Price’s Law on Nonstationary Spacetimes. Advances in Mathematics Volume 230, Issue 3, p 995-1028. Zbl1246.83070MR2921169
36. H. Ringström Future stability of the Einstein-non linear scalar field system Invent. Math. 173 (2008), no. 1, 123–208 Zbl1140.83314MR2403395
37. Sterbenz J., Tataru D. Local energy decay for Maxwell fields part I : Spherically symmetric black-hole backgrounds. http://arxiv.org/abs/1305.5261. Zbl1318.83006
38. J. Szeftel, Parametrix for wave equations on a rough background I : regularity of the phase at initial time. http://arxiv.org/abs/1204.1768, 145 pp. 
39. J. Szeftel, Parametrix for wave equations on a rough background II : control of the parametrix at initial time. http://arxiv.org/abs/1204.1769, 84 pp. 
40. J. Szeftel, Parametrix for wave equations on a rough background III : space-time regularity of the phase. http://arxiv.org/abs/1204.1770, 276 pp. 
41. J. Szeftel, Parametrix for wave equations on a rough background IV : Control of the error term. http://arxiv.org/abs/1204.1771, 284 pp. 
42. J. Szeftel, Sharp Strichartz estimates for the wave equation on a rough background. http://arxiv.org/abs/1301.0112, 30 pp. 
43. Tataru D., Local decay of waves on asymptotically flat stationary space-times. Amer. J. Math. 135 (2013), no. 2, 361-401. Zbl1266.83033MR3038715
44. Tataru D., Tohaneanu M. Local energy estimate on Kerr black hole backgrounds. Int. Math. Res. Not.2011 (2011), 248–292. Zbl1209.83028MR2764864
45. Vasy, A. The wave equation on asymptotically Anti-de-Sitter spaces. Analysis and PDE. Vol. 5 (2012), No. 1, 81-144 Zbl1277.35014MR2957552
46. Warnick, C. The massive wave equation in asymptotically AdS spacetimes. to appear in Comm. Math. Phys. (2012), http://arxiv.org/abs/1202.3445. Zbl1271.83021MR3089665