Abstract
We investigate whether arbitrarily small perturbations in global AdS space are generically unstable and collapse into black holes on the time scale set by gravitational interactions. We argue that current evidence, combined with our analysis, strongly suggests that a set of nonzero measure in the space of initial conditions does not collapse on this time scale. We perform an analysis in position space to study this puzzle, and our formalism allows us to directly study the vanishing-amplitude limit. We show that gravitational self-interaction leads to tidal deformations which are equally likely to focus or defocus energy, and we sketch the phase diagram accordingly. We also clarify the connection between gravitational evolution in global AdS and holographic thermalization.
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References
P. Bizon and A. Rostworowski, On weakly turbulent instability of anti-de Sitter space, Phys. Rev. Lett. 107 (2011) 031102 [arXiv:1104.3702] [INSPIRE].
H.P. de Oliveira, L.A. Pando Zayas and E.L. Rodrigues, A Kolmogorov-Zakharov Spectrum in AdS Gravitational Collapse, Phys. Rev. Lett. 111 (2013) 051101 [arXiv:1209.2369] [INSPIRE].
S.L. Liebling, Nonlinear collapse in the semilinear wave equation in AdS space, Phys. Rev. D 87 (2013) 081501 [arXiv:1212.6970] [INSPIRE].
O.J.C. Dias, G.T. Horowitz, D. Marolf and J.E. Santos, On the Nonlinear Stability of Asymptotically Anti-de Sitter Solutions, Class. Quant. Grav. 29 (2012) 235019 [arXiv:1208.5772] [INSPIRE].
M. Maliborski, Instability of Flat Space Enclosed in a Cavity, Phys. Rev. Lett. 109 (2012) 221101 [arXiv:1208.2934] [INSPIRE].
A. Buchel, L. Lehner and S.L. Liebling, Scalar Collapse in AdS, Phys. Rev. D 86 (2012) 123011 [arXiv:1210.0890] [INSPIRE].
A. Buchel, S.L. Liebling and L. Lehner, Boson stars in AdS spacetime, Phys. Rev. D 87 (2013) 123006 [arXiv:1304.4166] [INSPIRE].
P. Bizon, Is AdS stable?, Gen. Rel. Grav. 46 (2014) 1724 [arXiv:1312.5544] [INSPIRE].
M. Maliborski and A. Rostworowski, Lecture Notes on Turbulent Instability of Anti-de Sitter Spacetime, Int. J. Mod. Phys. A 28 (2013) 1340020 [arXiv:1308.1235] [INSPIRE].
M. Maliborski and A. Rostworowski, Time-Periodic Solutions in an Einstein AdS-Massless-Scalar-Field System, Phys. Rev. Lett. 111 (2013) 051102 [arXiv:1303.3186] [INSPIRE].
V. Balasubramanian, A. Buchel, S.R. Green, L. Lehner and S.L. Liebling, Holographic Thermalization, Stability of Anti-de Sitter Space and the Fermi-Pasta-Ulam Paradox, Phys. Rev. Lett. 113 (2014) 071601 [arXiv:1403.6471] [INSPIRE].
M. Maliborski and A. Rostworowski, What drives AdS spacetime unstable?, Phys. Rev. D 89 (2014) 124006 [arXiv:1403.5434] [INSPIRE].
G.T. Horowitz and J.E. Santos, Geons and the Instability of Anti-de Sitter Spacetime, arXiv:1408.5906 [INSPIRE].
O.J.C. Dias, G.T. Horowitz and J.E. Santos, Gravitational Turbulent Instability of Anti-de Sitter Space, Class. Quant. Grav. 29 (2012) 194002 [arXiv:1109.1825] [INSPIRE].
P. Bizon and A. Rostworowski, Comment on “Holographic Thermalization, Stability of Anti-de Sitter Space and the Fermi-Pasta-Ulam Paradox”, Phys. Rev. Lett. 115 (2015) 049101 [arXiv:1410.2631] [INSPIRE].
B. Craps, O. Evnin and J. Vanhoof, Renormalization group, secular term resummation and AdS (in)stability, JHEP 10 (2014) 48 [arXiv:1407.6273] [INSPIRE].
S. Trotzky, Y.A. Chen, A. Flesch, I.P. McCulloch, U. Schollwöck, J. Eisert and I. Bloch, Probing the relaxation towards equilibrium in an isolated strongly correlated one-dimensional Bose gas, Nature Physics 8 (2012) 325 [arXiv:1101.2659].
M. Gring et al., Relaxation and Prethermalization in an Isolated Quantum System, Science 337 (2012) 1318 [arXiv:1112.0013].
A.D. Rendall, Convergent and divergent perturbation series and the post-Minkowskian approximation scheme, Class. Quant. Grav. 7 (1990) 803.
P. Bizon, T. Chmaj and A. Rostworowski, Late-time tails of a self-gravitating massless scalar field revisited, Class. Quant. Grav. 26 (2009) 175006 [arXiv:0812.4333] [INSPIRE].
P. Basu, C. Krishnan and A. Saurabh, A Stochasticity Threshold in Holography and and the Instability of AdS, Int. J. Mod. Phys. A 30 (2015) 1550128 [arXiv:1408.0624] [INSPIRE].
J. Abajo-Arrastia, E. da Silva, E. Lopez, J. Mas and A. Serantes, Holographic Relaxation of Finite Size Isolated Quantum Systems, JHEP 05 (2014) 126 [arXiv:1403.2632] [INSPIRE].
M.A. Amin, E.A. Lim and I.-S. Yang, A scattering theory of ultrarelativistic solitons, Phys. Rev. D 88 (2013) 105024 [arXiv:1308.0606] [INSPIRE].
M.A. Amin, E.A. Lim and I.-S. Yang, Clash of Kinks: Phase Shifts in Colliding Nonintegrable Solitons, Phys. Rev. Lett. 111 (2013) 224101 [arXiv:1308.0605] [INSPIRE].
P. Bizon and J. Jalmuzna, Globally regular instability of AdS 3, Phys. Rev. Lett. 111 (2013) 041102 [arXiv:1306.0317] [INSPIRE].
J. Jalmuzna, Three-dimensional Gravity and Instability of AdS 3, Acta Phys. Polon. B 44 (2013) 2603 [arXiv:1311.7409] [INSPIRE].
S. Lin and E. Shuryak, Toward the AdS/CFT Gravity Dual for High Energy Collisions. 3. Gravitationally Collapsing Shell and Quasiequilibrium, Phys. Rev. D 78 (2008) 125018 [arXiv:0808.0910] [INSPIRE].
S. Bhattacharyya and S. Minwalla, Weak Field Black Hole Formation in Asymptotically AdS Spacetimes, JHEP 09 (2009) 034 [arXiv:0904.0464] [INSPIRE].
T. Albash and C.V. Johnson, Evolution of Holographic Entanglement Entropy after Thermal and Electromagnetic Quenches, New J. Phys. 13 (2011) 045017 [arXiv:1008.3027] [INSPIRE].
V. Balasubramanian et al., Holographic Thermalization, Phys. Rev. D 84 (2011) 026010 [arXiv:1103.2683] [INSPIRE].
S.W. Hawking and D.N. Page, Thermodynamics of Black Holes in anti-de Sitter Space, Commun. Math. Phys. 87 (1983) 577 [INSPIRE].
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Dimitrakopoulos, F.V., Freivogel, B., Lippert, M. et al. Position space analysis of the AdS (in)stability problem. J. High Energ. Phys. 2015, 77 (2015). https://doi.org/10.1007/JHEP08(2015)077
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DOI: https://doi.org/10.1007/JHEP08(2015)077