Abstract
We consider an Einstein-scalar field model which is a consistent truncation of \( \mathcal{N} \) = 8 D = 4 gauged supergravity, the scalar field possessing a potential which is unbounded from below and a tachyonic mass above the Breitenlohner-Freedman bound. We investigate the spherically symmetric asymptotically anti-de Sitter soliton and black hole solutions, with the aim of clarifying the asymptotics and the possible boundary conditions at infinity. The emerging picture is contrasted with that found for an Einstein-scalar field model with the same scalar mass and a quartic selfinteraction term. We also provide arguments for the existence of solitonic solutions which can be viewed as non-linear continuation of the (probe) scalar multipolar clouds, with emphasis on the dipole case. Apart from numerical results, exact solutions are found for solitons with a monopole and dipole scalar field, as perturbations around the AdS background.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
A. Salam and J.A. Strathdee, A Steeply Rising Potential in Tensor Gauge Theory, Phys. Lett. B 67 (1977) 429 [INSPIRE].
S.J. Avis, C.J. Isham and D. Storey, Quantum Field Theory in anti-De Sitter Space-Time, Phys. Rev. D 18 (1978) 3565 [INSPIRE].
J.M. Maldacena, The Large N limit of superconformal field theories and supergravity, Adv. Theor. Math. Phys. 2 (1998) 231 [hep-th/9711200] [INSPIRE].
E. Witten, Anti-de Sitter space and holography, Adv. Theor. Math. Phys. 2 (1998) 253 [hep-th/9802150] [INSPIRE].
S.S. Gubser, I.R. Klebanov and A.M. Polyakov, Gauge theory correlators from noncritical string theory, Phys. Lett. B 428 (1998) 105 [hep-th/9802109] [INSPIRE].
O. Aharony et al., Large N field theories, string theory and gravity, Phys. Rept. 323 (2000) 183 [hep-th/9905111] [INSPIRE].
T. Hertog and G.T. Horowitz, Designer gravity and field theory effective potentials, Phys. Rev. Lett. 94 (2005) 221301 [hep-th/0412169] [INSPIRE].
E. Witten, Multitrace operators, boundary conditions, and AdS/CFT correspondence, hep-th/0112258 [INSPIRE].
M. Henneaux, C. Martinez, R. Troncoso and J. Zanelli, Asymptotic behavior and Hamiltonian analysis of anti-de Sitter gravity coupled to scalar fields, Annals Phys. 322 (2007) 824 [hep-th/0603185] [INSPIRE].
H. Lü, Y. Pang and C.N. Pope, AdS Dyonic Black Hole and its Thermodynamics, JHEP 11 (2013) 033 [arXiv:1307.6243] [INSPIRE].
T. Hertog and S. Hollands, Stability in designer gravity, Class. Quant. Grav. 22 (2005) 5323 [hep-th/0508181] [INSPIRE].
B. de Wit and H. Nicolai, The Consistency of the S7 Truncation in D = 11 Supergravity, Nucl. Phys. B 281 (1987) 211 [INSPIRE].
M.J. Duff and J.T. Liu, Anti-de Sitter black holes in gauged N = 8 supergravity, Nucl. Phys. B 554 (1999) 237 [hep-th/9901149] [INSPIRE].
M. Cvetic et al., Embedding AdS black holes in ten-dimensions and eleven-dimensions, Nucl. Phys. B 558 (1999) 96 [hep-th/9903214] [INSPIRE].
G.W. Gibbons, M.J. Perry and C.N. Pope, Bulk/boundary thermodynamic equivalence, and the Bekenstein and cosmic-censorship bounds for rotating charged AdS black holes, Phys. Rev. D 72 (2005) 084028 [hep-th/0506233] [INSPIRE].
M. Henneaux, C. Martinez, R. Troncoso and J. Zanelli, Black holes and asymptotics of 2+1 gravity coupled to a scalar field, Phys. Rev. D 65 (2002) 104007 [hep-th/0201170] [INSPIRE].
M. Henneaux, C. Martinez, R. Troncoso and J. Zanelli, Asymptotically anti-de Sitter spacetimes and scalar fields with a logarithmic branch, Phys. Rev. D 70 (2004) 044034 [hep-th/0404236] [INSPIRE].
T. Hertog and K. Maeda, Black holes with scalar hair and asymptotics in N = 8 supergravity, JHEP 07 (2004) 051 [hep-th/0404261] [INSPIRE].
T. Hertog and G.T. Horowitz, Towards a big crunch dual, JHEP 07 (2004) 073 [hep-th/0406134] [INSPIRE].
T. Hertog and K. Maeda, Stability and thermodynamics of AdS black holes with scalar hair, Phys. Rev. D 71 (2005) 024001 [hep-th/0409314] [INSPIRE].
A. Anabalon, T. Andrade, D. Astefanesei and R. Mann, Universal Formula for the Holographic Speed of Sound, Phys. Lett. B 781 (2018) 547 [arXiv:1702.00017] [INSPIRE].
G.T. Horowitz and V.E. Hubeny, CFT description of small objects in AdS, JHEP 10 (2000) 027 [hep-th/0009051] [INSPIRE].
G.W. Gibbons and S.W. Hawking, Action Integrals and Partition Functions in Quantum Gravity, Phys. Rev. D 15 (1977) 2752 [INSPIRE].
D. Marolf and S.F. Ross, Boundary Conditions and New Dualities: Vector Fields in AdS/CFT, JHEP 11 (2006) 085 [hep-th/0606113] [INSPIRE].
A. Anabalon, D. Astefanesei, D. Choque and C. Martinez, Trace Anomaly and Counterterms in Designer Gravity, JHEP 03 (2016) 117 [arXiv:1511.08759] [INSPIRE].
A.J. Amsel and D. Marolf, Energy Bounds in Designer Gravity, Phys. Rev. D 74 (2006) 064006 [Erratum ibid. 75 (2007) 029901] [hep-th/0605101] [INSPIRE].
A. Anabalon, D. Astefanesei and C. Martinez, Mass of asymptotically anti-de Sitter hairy spacetimes, Phys. Rev. D 91 (2015) 041501 [arXiv:1407.3296] [INSPIRE].
M. Henningson and K. Skenderis, The Holographic Weyl anomaly, JHEP 07 (1998) 023 [hep-th/9806087] [INSPIRE].
V. Balasubramanian and P. Kraus, A Stress tensor for Anti-de Sitter gravity, Commun. Math. Phys. 208 (1999) 413 [hep-th/9902121] [INSPIRE].
K. Skenderis, Asymptotically Anti-de Sitter space-times and their stress energy tensor, Int. J. Mod. Phys. A 16 (2001) 740 [hep-th/0010138] [INSPIRE].
M. Taylor, More on counterterms in the gravitational action and anomalies, hep-th/0002125 [INSPIRE].
J. Gegenberg, C. Martinez and R. Troncoso, A Finite action for three-dimensional gravity with a minimally coupled scalar field, Phys. Rev. D 67 (2003) 084007 [hep-th/0301190] [INSPIRE].
E. Radu and D.H. Tchrakian, New hairy black hole solutions with a dilaton potential, Class. Quant. Grav. 22 (2005) 879 [hep-th/0410154] [INSPIRE].
H. Lu, C.N. Pope and Q. Wen, Thermodynamics of AdS Black Holes in Einstein-Scalar Gravity, JHEP 03 (2015) 165 [arXiv:1408.1514] [INSPIRE].
W. Schönauer and R. Weiß, Efficient vectorizable PDE solvers, J. Comput. Appl. Math. 27 (1989) 279.
M. Schauder, R. Weiß and W. Schönauer, The CADSOL Program Package, Universität Karlsruhe, Interner Bericht Nr. 46/92 (1992).
C. Herdeiro and E. Radu, Anti-de-Sitter regular electric multipoles: Towards Einstein-Maxwell-AdS solitons, Phys. Lett. B 749 (2015) 393 [arXiv:1507.04370] [INSPIRE].
M.S. Costa et al., Polarised Black Holes in AdS, Class. Quant. Grav. 33 (2016) 115011 [arXiv:1511.08505] [INSPIRE].
C.A.R. Herdeiro and E. Radu, Static Einstein-Maxwell black holes with no spatial isometries in AdS space, Phys. Rev. Lett. 117 (2016) 221102 [arXiv:1606.02302] [INSPIRE].
R.C. Myers, Stress tensors and Casimir energies in the AdS/CFT correspondence, Phys. Rev. D 60 (1999) 046002 [hep-th/9903203] [INSPIRE].
C.A.R. Herdeiro and E. Radu, Asymptotically flat black holes with scalar hair: a review, Int. J. Mod. Phys. D 24 (2015) 1542014 [arXiv:1504.08209] [INSPIRE].
M. Headrick, S. Kitchen and T. Wiseman, A New approach to static numerical relativity, and its application to Kaluza-Klein black holes, Class. Quant. Grav. 27 (2010) 035002 [arXiv:0905.1822] [INSPIRE].
A. Adam, S. Kitchen and T. Wiseman, A numerical approach to finding general stationary vacuum black holes, Class. Quant. Grav. 29 (2012) 165002 [arXiv:1105.6347] [INSPIRE].
Ó.J.C. Dias, J.E. Santos and B. Way, Numerical Methods for Finding Stationary Gravitational Solutions, Class. Quant. Grav. 33 (2016) 133001 [arXiv:1510.02804] [INSPIRE].
P. Breitenlohner and D.Z. Freedman, Stability in Gauged Extended Supergravity, Annals Phys. 144 (1982) 249 [INSPIRE].
C. Martinez, R. Troncoso and J. Zanelli, Exact black hole solution with a minimally coupled scalar field, Phys. Rev. D 70 (2004) 084035 [hep-th/0406111] [INSPIRE].
A. Anabalón, D. Astefanesei, A. Gallerati and M. Trigiante, Hairy Black Holes and Duality in an Extended Supergravity Model, JHEP 04 (2018) 058 [arXiv:1712.06971] [INSPIRE].
A. Donos and J.P. Gauntlett, Superfluid black branes in AdS4 × S7, JHEP 06 (2011) 053 [arXiv:1104.4478] [INSPIRE].
N. Bobev, N. Halmagyi, K. Pilch and N.P. Warner, Supergravity Instabilities of Non-Supersymmetric Quantum Critical Points, Class. Quant. Grav. 27 (2010) 235013 [arXiv:1006.2546] [INSPIRE].
Z.-W. Chong, H. Lu and C.N. Pope, BPS geometries and AdS bubbles, Phys. Lett. B 614 (2005) 96 [hep-th/0412221] [INSPIRE].
J.P. Gauntlett, J. Sonner and T. Wiseman, Holographic superconductivity in M-Theory, Phys. Rev. Lett. 103 (2009) 151601 [arXiv:0907.3796] [INSPIRE].
J.P. Gauntlett, J. Sonner and T. Wiseman, Quantum Criticality and Holographic Superconductors in M-theory, JHEP 02 (2010) 060 [arXiv:0912.0512] [INSPIRE].
S.A. Gentle, M. Rangamani and B. Withers, A Soliton Menagerie in AdS, JHEP 05 (2012) 106 [arXiv:1112.3979] [INSPIRE].
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher’s Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
ArXiv ePrint: 2210.09431
Rights and permissions
Open Access . This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.
About this article
Cite this article
Astefanesei, D., Huang, H., Kunz, J. et al. Einstein-scalar field solutions in AdS spacetime: clouds, boundary conditions, and scalar multipoles. J. High Energ. Phys. 2023, 174 (2023). https://doi.org/10.1007/JHEP03(2023)174
Received:
Revised:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP03(2023)174