On the nonlinear stability of asymptotically anti-de Sitter solutions

Classical and Quantum Gravity

Volumn 29, Issue 23, 2012, Pages

  Dias, Óscar J C ^a   Horowitz, Gary T ^b   Marolf, Don ^b   Santos, Jorge E ^b  

^a CEA SACLAY   (France)

^b UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 84868557369     PISSN: 02649381     EISSN: 13616382     Source Type: Journal    
DOI: 10.1088/0264-9381/29/23/235019     Document Type: Article

References (41)

1. Bizon P and Rostworowski A 2011 On weakly turbulent instability of anti-de Sitter space Phys. Rev. Lett. 107 031102 (arXiv:1104.3702 [gr-qc])
2. Jalmuzna J, Rostworowski A and Bizon P 2011 A comment on AdS collapse of a scalar field in higher dimensions Phys. Rev. D 84 085021 (arXiv:1108.4539 [gr-qc])
3. Dias O J C, Horowitz G T and Santos J E 2011 Gravitational turbulent instability of anti-de Sitter space arXiv:1109.1825 [hep-th]
4. Anderson M T 2006 On the uniqueness and global dynamics of AdS spacetimes Class. Quantum Grav. 23 6935 (arXiv:hep-th/0605293)
5. Dafermos M 2012 private communication
6. Friedman J L, Schleich K and Witt D M 1993 Topological censorship Phys. Rev. Lett. 71 1486 (arXiv:gr-qc/9305017)
7. Friedman J L, Schleich K and Witt D M 1995 Topological censorship Phys. Rev. Lett. 75 1872 (erratum)
8. Liebling S L and Palenzuela C 2012 Dynamical boson stars Living Rev. Rel. 15 6 (arXiv:1202.5809 [gr-qc])
9. Colliander J, Keel M, Staffilani G, Takaoka H and Tao T 2010 Transfer of energy to high frequencies in the cubic defocusing nonlinear Schrödinger equation Invent. Math. 181 39
10. d arXiv:1010.5173 [math.AP]
11. Faou E, Gauckler L and Lubich C 2011 Sobolev stability of plane wave solutions to the cubic nonlinear Schrödinger equation on a torus arXiv:1109.2407 [math.AP]
12. Press W H and Teukolsky S A 1972 Floating orbits, superradiant scattering and the black-hole bomb Nature 238 211
13. Cardoso V, Chakrabarti S, Pani P, Berti E and Gualtieri L 2011 Floating and sinking: the imprint of massive scalars around rotating black holes Phys. Rev. Lett. 107 241101 (arXiv:1109.6021 [gr-qc])
14. Festuccia G and Liu H 2008 A Bohr-Sommerfeld quantization formula for quasinormal frequencies of AdS black holes arXiv:0811.1033 [gr-qc]
15. Berti E, Cardoso V and Pani P 2009 Breit-Wigner resonances and the quasinormal modes of anti-de Sitter black holes Phys. Rev. D 79 101501 (arXiv:0903.5311 [gr-qc])
16. Kodama H and Ishibashi A 2003 A master equation for gravitational perturbations of maximally symmetric black holes in higher dimensions Prog. Theor. Phys. 110 701-22 (arXiv:hep-th/0305147) (Pubitemid 37545250)
17. Boucher W, Gibbons G W and Horowitz G T 1984 A uniqueness theorem for anti-de Sitter space-time Phys. Rev. D 30 2447
18. Henneaux M and Teitelboim C 1985 Asymptotically anti-de Sitter Spaces Commun. Math. Phys. 98 391
19. Michalogiorgakis G and Pufu S S 2007 Low-lying gravitational modes in the scalar sector of the global AdS(4) black hole J. High Energy Phys. JHEP02(2007)023 (arXiv:hep-th/0612065)
20. Compere G and Marolf D 2008 Setting the boundary free in AdS/CFT Class. Quantum Grav. 25 195014 (arXiv:0805.1902 [hep-th])
21. Andrade T and Marolf D 2012 AdS/CFT beyond the unitarity bound J. High Energy Phys. JHEP01(2012)049 (arXiv:1105.6337 [hep-th])
22. Breitenlohner P and Freedman D Z 1982 Stability in gauged extended supergravity Ann. Phys. 144 249
23. Mezincescu L and Townsend P K 1985 Stability at a local maximum in higher dimensional anti-de Sitter space and applications to supergravity Ann. Phys. 160 406
24. Hawking S W, Hunter C J and Taylor M 1999 Rotation and the AdS/CFT correspondence Phys. Rev. D 59 064005 (arXiv:hep-th/9811056)
25. Gibbons G W, Lu H, Page D N and Pope C N 2005 The general Kerr-de Sitter metrics in all dimensions J. Geom. Phys. 53 49 (arXiv:hep-th/0404008) (Pubitemid 39518878)
26. Gibbons G W, Lu H, Page D N and Pope C N 2004 Rotating black holes in higher dimensions with a cosmological constant Phys. Rev. Lett. 93 171102 (arXiv:hep-th/0409155)
27. Kunduri H K, Lucietti J and Reall H S 2006 Gravitational perturbations of higher dimensional rotating black holes: tensor perturbations Phys. Rev. D 74 084021 (arXiv:hep-th/0606076) (Pubitemid 44601922)
28. Hoxha P, Martinez-Acosta R R and Pope C N 2000 Kaluza-Klein consistency, Killing vectors, and Kahler spaces Class. Quantum Grav. 17 4207 (arXiv:hep-th/0005172)
29. Bieri L 2009 An extension of the stability theorem of the Minkowski space in general relativity arXiv:0904.0620 [gr-qc]
30. Rodnianski I and Dafermos M 2012 private communication
31. Dias O J C and Santos J E to appear
32. Liebling S 2012 As reported in Exploring AdS/CFT Dualities in Dynamical Settings Perimeter Institute Workshop
33. Buchel A, Lehner L and Liebling S to appear
34. Ishibashi A and Maeda K 2012 Singularities in asymptotically anti-de Sitter spacetimes arXiv:1208.1563 [hep-th]
35. Bhattacharyya S, Hubeny V, Minwalla S and Rangamani M 2008 Nonlinear fluid dynamics from gravity J. High Energy Phys. JHEP02(2008)045 (arXiv:0712.2456 [hep-th]
36. Lehner L 2012 As reported in Exploring AdS/CFT Dualities in Dynamical Settings Perimeter Institute Workshop
37. Carrasco F, Lehner L, Myers R C, Reula O and Singh A 2012 Turbulent flows for relativistic conformal fluids in 2+1 dimensions arXiv:1210.6702 [hep-th]
38. Amsel A J, Hertog T, Hollands S and Marolf D 2007 A tale of two superpotentials: stability and instability in designer gravity Phys. Rev. D 75 084008 (arXiv:hep-th/0701038)
39. Amsel A J, Hertog T, Hollands S and Marolf D 2008 A tale of two superpotentials: stability and instability in designer gravity Phys. Rev. D 77 049903 (erratum)
40. Witten E 1998 Anti-de Sitter space, thermal phase transition, and confinement in gauge theories Adv. Theor. Math. Phys. 2 505 (arXiv:hep-th/ 9803131)
41. Horowitz G T and Myers R C 1998 The AdS/CFT correspondence and a new positive energy conjecture for general relativity Phys. Rev. D 59 026005 (arXiv:hep-th/9808079)