Abstract
We develop the large D limit of general relativity for spherically symmetric scalar fields in both asymptotically flat and asymptotically anti-de Sitter spaces. The leading order equations in the 1/D expansion can be solved analytically, providing a large D description of oscillating soliton stars. When the amplitude reaches a critical threshold, certain divergences occur which we interpret as signal of horizon formation. We estimate the size of the resulting black hole and obtain a scaling exponent. We speculate on some connections to Choptuik critical collapse.
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R. Emparan, R. Suzuki and K. Tanabe, The large D limit of general relativity, JHEP 06 (2013) 009 [arXiv:1302.6382] [INSPIRE].
R. Emparan, R. Suzuki and K. Tanabe, Instability of rotating black holes: large D analysis, JHEP 06 (2014) 106 [arXiv:1402.6215] [INSPIRE].
T. Andrade, R. Emparan and D. Licht, Rotating black holes and black bars at large D, JHEP 09 (2018) 107 [arXiv:1807.01131] [INSPIRE].
R. Emparan, R. Suzuki and K. Tanabe, Evolution and end point of the black string instability: large D solution, Phys. Rev. Lett. 115 (2015) 091102 [arXiv:1506.06772] [INSPIRE].
M. Rozali and A. Vincart-Emard, On brane instabilities in the large D limit, JHEP 08 (2016) 166 [arXiv:1607.01747] [INSPIRE].
Y. Dandekar, S. Mazumdar, S. Minwalla and A. Saha, Unstable ‘black branes’ from scaled membranes at large D, JHEP 12 (2016) 140 [arXiv:1609.02912] [INSPIRE].
R. Emparan et al., Phases and stability of non-uniform black strings, JHEP 05 (2018) 104 [arXiv:1802.08191] [INSPIRE].
M. Rozali, E. Sabag and A. Yarom, Holographic turbulence in a large number of dimensions, JHEP 04 (2018) 065 [arXiv:1707.08973] [INSPIRE].
R. Emparan and K. Tanabe, Universal quasinormal modes of large D black holes, Phys. Rev. D 89 (2014) 064028 [arXiv:1401.1957] [INSPIRE].
R. Emparan, R. Suzuki and K. Tanabe, Decoupling and non-decoupling dynamics of large D black holes, JHEP 07 (2014) 113 [arXiv:1406.1258] [INSPIRE].
R. Emparan, R. Suzuki and K. Tanabe, Quasinormal modes of (Anti-)de Sitter black holes in the 1/Dexpansion, JHEP 04 (2015) 085 [arXiv:1502.02820] [INSPIRE].
R. Emparan et al., Effective theory of black holes in the 1/D expansion, JHEP 06 (2015) 159 [arXiv:1504.06489] [INSPIRE].
R. Emparan et al., Hydro-elastic complementarity in black branes at large D, JHEP 06 (2016) 117 [arXiv:1602.05752] [INSPIRE].
S. Bhattacharyya, A. De, S. Minwalla, R. Mohan and A. Saha, A membrane paradigm at large D, JHEP 04 (2016) 076 [arXiv:1504.06613] [INSPIRE].
S. Bhattacharyya, M. Mandlik, S. Minwalla and S. Thakur, A charged membrane paradigm at large D, JHEP 04 (2016) 128 [arXiv:1511.03432] [INSPIRE].
Y. Dandekar et al., The large D black hole membrane paradigm at first subleading order, JHEP 12 (2016) 113 [arXiv:1607.06475] [INSPIRE].
S. Bhattacharyya et al., Currents and radiation from the large D black hole membrane, JHEP 05 (2017) 098 [arXiv:1611.09310] [INSPIRE].
Y. Dandekar et al., An action for and hydrodynamics from the improved large D membrane, JHEP 09 (2018) 137 [arXiv:1712.09400] [INSPIRE].
R. Emparan and K. Tanabe, Holographic superconductivity in the large D expansion, JHEP 01 (2014) 145 [arXiv:1312.1108] [INSPIRE].
M.W. Choptuik, Universality and scaling in gravitational collapse of a massless scalar field, Phys. Rev. Lett. 70 (1993) 9 [INSPIRE].
D. Garfinkle, C. Cutler and G.C. Duncan, Choptuik scaling in six-dimensions, Phys. Rev. D 60 (1999) 104007 [gr-qc/9908044] [INSPIRE].
E. Sorkin and Y. Oren, On Choptuik’s scaling in higher dimensions, Phys. Rev. D 71 (2005) 124005 [hep-th/0502034] [INSPIRE].
J. Bland et al., Dimension-dependence of the critical exponent in spherically symmetric gravitational collapse, Class. Quant. Grav. 22 (2005) 5355 [gr-qc/0507088] [INSPIRE].
C. Gundlach, Understanding critical collapse of a scalar field, Phys. Rev. D 55 (1997) 695 [gr-qc/9604019] [INSPIRE].
E. Seidel and W.M. Suen, Oscillating soliton stars, Phys. Rev. Lett. 66 (1991) 1659 [INSPIRE].
T.D. Lee and Y. Pang, Nontopological solitons, Phys. Rept. 221 (1992) 251 [INSPIRE].
F.E. Schunck and E.W. Mielke, General relativistic boson stars, Class. Quant. Grav. 20 (2003) R301 [arXiv:0801.0307] [INSPIRE].
S.L. Liebling and C. Palenzuela, Dynamical Boson Stars, Living Rev. Rel. 15 (2012) 6 [arXiv:1202.5809] [INSPIRE].
M. Dafermos and G. Holzegel, Dynamic instability of solitons in 4 + 1 dimensional gravity with negative cosmological constant, seminar held at the Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Cambridge, U.K. (2006).
M. Dafermos, The black hole stability problem, talk given at the Newton Institute, University of Cambridge, Cambridge, U.K. (2006).
P. Bizon and A. Rostworowski, On weakly turbulent instability of Anti-de Sitter space, Phys. Rev. Lett. 107 (2011) 031102 [arXiv:1104.3702] [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 and A. Rostworowski, Time-periodic solutions in an Einstein AdS-massless-scalar-field system, Phys. Rev. Lett. 111 (2013) 051102 [arXiv:1303.3186] [INSPIRE].
A. Buchel, S.L. Liebling and L. Lehner, Boson stars in AdS spacetime, Phys. Rev. D 87 (2013) 123006 [arXiv:1304.4166] [INSPIRE].
V. Balasubramanian et al., Holographic thermalization, stability of Anti-de Sitter space and the Fermi-Pasta-Ulam paradox, Phys. Rev. Lett. 113 (2014) 071601 [arXiv:1403.6471] [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].
V. Balasubramanian et al., Reply to comment on “Holographic thermalization, stability of Anti-de Sitter space and the Fermi-Pasta-Ulam paradox”, Phys. Rev. Lett. 115 (2015) 049102 [arXiv:1506.07907] [INSPIRE].
F. Dimitrakopoulos and I.-S. Yang, Conditionally extended validity of perturbation theory: persistence of AdS stability islands, Phys. Rev. D 92 (2015) 083013 [arXiv:1507.02684] [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].
M. Choptuik, J.E. Santos and B. Way, Charting islands of stability with multioscillators in Anti-de Sitter space, Phys. Rev. Lett. 121 (2018) 021103 [arXiv:1803.02830] [INSPIRE].
G. Fodor, P. Forgàcs and P. Grandclément, Self-gravitating scalar breathers with negative cosmological constant, Phys. Rev. D 92 (2015) 025036 [arXiv:1503.07746] [INSPIRE].
O.J.C. Dias, G.T. Horowitz and J.E. Santos, Black holes with only one Killing field, JHEP 07 (2011) 115 [arXiv:1105.4167] [INSPIRE].
M.W. Choptuik, A.J.C. Dias, J.E. Santos and B. Way, Collapse and nonlinear instability of AdS space with angular momentum, Phys. Rev. Lett. 119 (2017) 191104 [arXiv:1706.06101] [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].
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].
J.B. Bland, Dimension dependence of the critical phenomena in gravitational collapse of massless scalar field, Ph.D. thesis, University of Manitoba, Manitoba, Canada (2007).
M.D. Roberts, Scalar field counterexamples to the cosmic censorship hypothesis, Gen. Rel. Grav. 21 (1989) 907 [INSPIRE].
A.V. Frolov, Selfsimilar collapse of scalar field in higher dimensions, Class. Quant. Grav. 16 (1999) 407 [gr-qc/9806112] [INSPIRE].
A.V. Frolov, Perturbations and critical behavior in the selfsimilar gravitational collapse of a massless scalar field, Phys. Rev. D 56 (1997) 6433 [gr-qc/9704040] [INSPIRE].
A.V. Frolov, Critical collapse beyond spherical symmetry: general perturbations of the Roberts solution, Phys. Rev. D 59 (1999) 104011 [gr-qc/9811001] [INSPIRE].
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Rozali, M., Way, B. Gravitating scalar stars in the large D limit. J. High Energ. Phys. 2018, 106 (2018). https://doi.org/10.1007/JHEP11(2018)106
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DOI: https://doi.org/10.1007/JHEP11(2018)106