Abstract
We consider five-dimensional, vacuum Einstein equations with negative cosmological constant within cohomogenity-two biaxial Bianchi IX ansatz. This model allows to investigate the stability of AdS without adding any matter to the energy-momentum tensor, thus analyzing instability of genuine gravitational degrees of freedom. We derive the resonant system and identify vanishing secular terms. The results resemble those obtained for Einstein equations coupled to a spherically-symmetric, massless scalar field, backing the evidence that the scalar field model captures well the relevant features of AdS instability problem. We also list recurrence relations for the interaction coefficients of the resonant system, which might be useful in both numerical simulations and further analytical studies.
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References
P. Bizoń and A. Rostworowski, On weakly turbulent instability of anti-de Sitter space, Phys. Rev. Lett. 107 (2011) 031102 [arXiv:1104.3702] [INSPIRE].
J. Ja-lmużna, A. Rostworowski and P. Bizoń, A Comment on AdS collapse of a scalar field in higher dimensions, Phys. Rev. D 84 (2011) 085021 [arXiv:1108.4539] [INSPIRE].
G. Moschidis, A proof of the instability of AdS for the Einstein-null dust system with an inner mirror, arXiv:1704.08681 [INSPIRE].
G. Moschidis, A proof of the instability of AdS for the Einstein-massless Vlasov system, arXiv:1812.04268 [INSPIRE].
F.V. Dimitrakopoulos, B. Freivogel, M. Lippert and I.-S. Yang, Position space analysis of the AdS (in)stability problem, JHEP 08 (2015) 077 [arXiv:1410.1880] [INSPIRE].
N. Deppe, A. Kolly, A. Frey and G. Kunstatter, Stability of AdS in Einstein Gauss Bonnet Gravity, Phys. Rev. Lett. 114 (2015) 071102 [arXiv:1410.1869] [INSPIRE].
N. Deppe and A.R. Frey, Classes of Stable Initial Data for Massless and Massive Scalars in Anti-de Sitter Spacetime, JHEP 12 (2015) 004 [arXiv:1508.02709] [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].
M. Maliborski, Dynamics of Nonlinear Waves on Bounded Domains, Ph.D. Thesis, Jagiellonian University, Kraków Poland (2014) [arXiv:1603.00935] [INSPIRE].
A. Buchel, S.L. Liebling and L. Lehner, Boson stars in AdS spacetime, Phys. Rev. D 87 (2013) 123006 [arXiv:1304.4166] [INSPIRE].
G. Fodor, P. Forgács and P. Grandclément, Self-gravitating scalar breathers with negative cosmological constant, Phys. Rev. D 92 (2015) 025036 [arXiv:1503.07746] [INSPIRE].
Ó.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].
G.T. Horowitz and J.E. Santos, Geons and the Instability of Anti-de Sitter Spacetime, Surveys Diff. Geom. 20 (2015) 321 [arXiv:1408.5906] [INSPIRE].
G. Martinon, G. Fodor, P. Grandclément and P. Forgàcs, Gravitational geons in asymptotically anti-de Sitter spacetimes, Class. Quant. Grav. 34 (2017) 125012 [arXiv:1701.09100] [INSPIRE].
A. Rostworowski, Higher order perturbations of anti-de Sitter space and time-periodic solutions of vacuum Einstein equations, Phys. Rev. D 95 (2017) 124043 [arXiv:1701.07804] [INSPIRE].
G. Fodor and P. Forgács, Anti-de Sitter geon families, Phys. Rev. D 96 (2017) 084027 [arXiv:1708.09228] [INSPIRE].
B. Craps and O. Evnin, AdS (in)stability: an analytic approach, Fortsch. Phys. 64 (2016) 336 [arXiv:1510.07836] [INSPIRE].
H. Bantilan, P. Figueras, M. Kunesch and P. Romatschke, Nonspherically Symmetric Collapse in Asymptotically AdS Spacetimes, Phys. Rev. Lett. 119 (2017) 191103 [arXiv:1706.04199] [INSPIRE].
P. Bizoń and A. Rostworowski, Gravitational Turbulent Instability of AdS5 , Acta Phys. Polon. B 48 (2017) 1375 [arXiv:1710.03438] [INSPIRE].
P. Bizoń, T. Chmaj and B.G. Schmidt, Critical behavior in vacuum gravitational collapse in 4 + 1 dimensions, Phys. Rev. Lett. 95 (2005) 071102 [gr-qc/0506074] [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].
B. Craps, O. Evnin and J. Vanhoof, Renormalization group, secular term resummation and AdS (in)stability, JHEP 10 (2014) 048 [arXiv:1407.6273] [INSPIRE].
B. Craps, O. Evnin and J. Vanhoof, Renormalization, averaging, conservation laws and AdS (in)stability, JHEP 01 (2015) 108 [arXiv:1412.3249] [INSPIRE].
A. Buchel, S.R. Green, L. Lehner and S.L. Liebling, Conserved quantities and dual turbulent cascades in anti-de Sitter spacetime, Phys. Rev. D 91 (2015) 064026 [arXiv:1412.4761] [INSPIRE].
S.R. Green, A. Maillard, L. Lehner and S.L. Liebling, Islands of stability and recurrence times in AdS, Phys. Rev. D 92 (2015) 084001 [arXiv:1507.08261] [INSPIRE].
P. Bizoń, M. Maliborski and A. Rostworowski, Resonant Dynamics and the Instability of Anti-de Sitter Spacetime, Phys. Rev. Lett. 115 (2015) 081103 [arXiv:1506.03519] [INSPIRE].
F.V. Dimitrakopoulos, B. Freivogel, J.F. Pedraza and I.-S. Yang, Gauge dependence of the AdS instability problem, Phys. Rev. D 94 (2016) 124008 [arXiv:1607.08094] [INSPIRE].
N. Deppe, Resonant dynamics in higher dimensional anti-de Sitter spacetime, Phys. Rev. D 100 (2019) 124028 [arXiv:1606.02712] [INSPIRE].
P. Bizoń, B. Craps, O. Evnin, D. Hunik, V. Luyten and M. Maliborski, Conformal Flow on S3 and Weak Field Integrability in AdS4 , Commun. Math. Phys. 353 (2017) 1179 [arXiv:1608.07227] [INSPIRE].
A. Biasi, P. Bizoń and O. Evnin, Solvable cubic resonant systems, Commun. Math. Phys. 369 (2019) 433 [arXiv:1805.03634] [INSPIRE].
O. Evnin and W. Piensuk, Quantum resonant systems, integrable and chaotic, J. Phys. A 52 (2019) 025102 [arXiv:1808.09173] [INSPIRE].
A. Rostworowski, Towards a theory of nonlinear gravitational waves: A systematic approach to nonlinear gravitational perturbations in the vacuum, Phys. Rev. D 96 (2017) 124026 [arXiv:1705.02258] [INSPIRE].
Ó.J.C. Dias and J.E. Santos, AdS nonlinear instability: breaking spherical and axial symmetries, Class. Quant. Grav. 35 (2018) 185006 [arXiv:1705.03065] [INSPIRE].
A. Ishibashi and R.M. Wald, Dynamics in nonglobally hyperbolic static space-times. 3. Anti-de Sitter space-time, Class. Quant. Grav. 21 (2004) 2981 [hep-th/0402184] [INSPIRE].
M. Maliborski, private communication (2015).
B. Craps, O. Evnin and J. Vanhoof, Ultraviolet asymptotics and singular dynamics of AdS perturbations, JHEP 10 (2015) 079 [arXiv:1508.04943] [INSPIRE].
P. Bizoń 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].
N. Deppe, Resonant dynamics in higher dimensional anti-de Sitter spacetime, Phys. Rev. D 100 (2019) 124028 [arXiv:1606.02712] [INSPIRE].
M. Maliborski, private communication (2015).
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Hunik-Kostyra, D., Rostworowski, A. AdS instability: resonant system for gravitational perturbations of AdS5 in the cohomogeneity-two biaxial Bianchi IX ansatz. J. High Energ. Phys. 2020, 2 (2020). https://doi.org/10.1007/JHEP06(2020)002
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DOI: https://doi.org/10.1007/JHEP06(2020)002