Trace anomaly and counterterms in designer gravity

  • Andrés Anabalón
  • Dumitru Astefanesei
  • David Choque
  • Cristián Martínez
Open Access
Regular Article - Theoretical Physics


We construct concrete counterterms of the Balasubramanian-Kraus type for Einstein-scalar theories with designer gravity boundary conditions in AdS4, so that the total action is finite on-shell and satisfy a well defined variational principle. We focus on scalar fields with the conformal mass m 2 = −2l −2 and show that the holographic mass matches the Hamiltonian mass for any boundary conditions. We compute the trace anomaly of the dual field theory in the generic case, as well as when there exist logarithmic branches of non-linear origin. As expected, the anomaly vanishes for the boundary conditions that are AdS invariant. When the anomaly does not vanish, the dual stress tensor describes a thermal gas with an equation of state related to the boundary conditions of the scalar field. In the case of a vanishing anomaly, we recover the dual theory of a massless thermal gas. As an application of the formalism, we consider a general family of exact hairy black hole solutions that, for some particular values of the parameters in the moduli potential, contains solutions of four-dimensional gauged \( \mathcal{N}=8 \) supergravity and its ω-deformation. Using the AdS/CFT duality dictionary, they correspond to triple trace deformations of the dual field theory.


AdS-CFT Correspondence Black Holes Gauge-gravity correspondence 


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.


  1. [1]
    J.M. Maldacena, The Large-N limit of superconformal field theories and supergravity, [Adv. Theor. Math. Phys. 2 (1998) 231] [Int. J. Theor. Phys. 38 (1999) 1113] [hep-th/9711200] [INSPIRE].
  2. [2]
    M. Henningson and K. Skenderis, The Holographic Weyl anomaly, JHEP 07 (1998) 023 [hep-th/9806087] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  3. [3]
    V. Balasubramanian and P. Kraus, A Stress tensor for Anti-de Sitter gravity, Commun. Math. Phys. 208 (1999) 413 [hep-th/9902121] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  4. [4]
    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].
  5. [5]
    P. Breitenlohner and D.Z. Freedman, Positive Energy in anti-de Sitter Backgrounds and Gauged Extended Supergravity, Phys. Lett. B 115 (1982) 197 [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  6. [6]
    P. Breitenlohner and D.Z. Freedman, Stability in Gauged Extended Supergravity, Annals Phys. 144 (1982) 249 [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  7. [7]
    M. Henneaux, C. Martínez, 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].
  8. [8]
    G. Barnich, Conserved charges in gravitational theories: contribution from scalar fields, gr-qc/0211031 [INSPIRE].
  9. [9]
    M. Henneaux, C. Martínez, 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].
  10. [10]
    T. Hertog and K. Maeda, Black holes with scalar hair and asymptotics in N = 8 supergravity, JHEP 07 (2004) 051 [hep-th/0404261] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  11. [11]
    T. Hertog and G.T. Horowitz, Designer gravity and field theory effective potentials, Phys. Rev. Lett. 94 (2005) 221301 [hep-th/0412169] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  12. [12]
    M. Henneaux, C. Martínez, 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].
  13. [13]
    A.J. Amsel and D. Marolf, Energy Bounds in Designer Gravity, Phys. Rev. D 74 (2006) 064006 [Erratum ibid. D 75 (2007) 029901] [hep-th/0605101] [INSPIRE].
  14. [14]
    A. Anabalón, D. Astefanesei and C. Martínez, Mass of asymptotically anti-de Sitter hairy spacetimes, Phys. Rev. D 91 (2015) 041501 [arXiv:1407.3296] [INSPIRE].
  15. [15]
    E. Witten, Multitrace operators, boundary conditions and AdS/CFT correspondence, hep-th/0112258 [INSPIRE].
  16. [16]
    O. Aharony, G. Gur-Ari and N. Klinghoffer, The Holographic Dictionary for β-functions of Multi-trace Coupling Constants, JHEP 05 (2015) 031 [arXiv:1501.06664] [INSPIRE].MathSciNetCrossRefGoogle Scholar
  17. [17]
    A. Acena, A. Anabalón and D. Astefanesei, Exact hairy black brane solutions in AdS 5 and holographic RG flows, Phys. Rev. D 87 (2013) 124033 [arXiv:1211.6126] [INSPIRE].ADSGoogle Scholar
  18. [18]
    A. Aceña, A. Anabalón, D. Astefanesei and R. Mann, Hairy planar black holes in higher dimensions, JHEP 01 (2014) 153 [arXiv:1311.6065] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  19. [19]
    A. Anabalón and D. Astefanesei, On attractor mechanism of AdS 4 black holes, Phys. Lett. B 727 (2013) 568 [arXiv:1309.5863] [INSPIRE].ADSCrossRefMATHGoogle Scholar
  20. [20]
    Z.-Y. Fan and B. Chen, Exact formation of hairy planar black holes, arXiv:1512.09145 [INSPIRE].
  21. [21]
    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].ADSMathSciNetCrossRefMATHGoogle Scholar
  22. [22]
    K. Skenderis, Lecture notes on holographic renormalization, Class. Quant. Grav. 19 (2002) 5849 [hep-th/0209067] [INSPIRE].MathSciNetCrossRefMATHGoogle Scholar
  23. [23]
    J.D. Brown and J.W. York Jr., Quasilocal energy and conserved charges derived from the gravitational action, Phys. Rev. D 47 (1993) 1407 [gr-qc/9209012] [INSPIRE].
  24. [24]
    I. Papadimitriou, Multi-Trace Deformations in AdS/CFT: Exploring the Vacuum Structure of the Deformed CFT, JHEP 05 (2007) 075 [hep-th/0703152] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  25. [25]
    J. Aparicio, D. Grumiller, E. Lopez, I. Papadimitriou and S. Stricker, Bootstrapping gravity solutions, JHEP 05 (2013) 128 [arXiv:1212.3609] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  26. [26]
    S. Nojiri and S.D. Odintsov, Conformal anomaly for dilaton coupled theories from AdS/CFT correspondence, Phys. Lett. B 444 (1998) 92 [hep-th/9810008] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  27. [27]
    S. Nojiri, S.D. Odintsov and S. Ogushi, Finite action in d-5 gauged supergravity and dilatonic conformal anomaly for dual quantum field theory, Phys. Rev. D 62 (2000) 124002 [hep-th/0001122] [INSPIRE].ADSMathSciNetGoogle Scholar
  28. [28]
    A. Ashtekar and S. Das, Asymptotically Anti-de Sitter space-times: Conserved quantities, Class. Quant. Grav. 17 (2000) L17 [hep-th/9911230] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  29. [29]
    A. Ashtekar and A. Magnon, Asymptotically anti-de Sitter space-times, Class. Quant. Grav. 1 (1984) L39 [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  30. [30]
    D.D.K. Chow and G. Compère, Dyonic AdS black holes in maximal gauged supergravity, Phys. Rev. D 89 (2014) 065003 [arXiv:1311.1204] [INSPIRE].ADSGoogle Scholar
  31. [31]
    A. Anabalón and D. Astefanesei, Black holes in ω-defomed gauged N = 8 supergravity, Phys. Lett. B 732 (2014) 137 [arXiv:1311.7459] [INSPIRE].ADSCrossRefGoogle Scholar
  32. [32]
    G. Dall’Agata, G. Inverso and M. Trigiante, Evidence for a family of SO(8) gauged supergravity theories, Phys. Rev. Lett. 109 (2012) 201301 [arXiv:1209.0760] [INSPIRE].ADSCrossRefGoogle Scholar
  33. [33]
    J. Tarrío and O. Varela, Electric/magnetic duality and RG flows in AdS4/CFT3, JHEP 01 (2014) 071 [arXiv:1311.2933] [INSPIRE].
  34. [34]
    G. Dibitetto, A. Guarino and D. Roest, Lobotomy of Flux Compactifications, JHEP 05 (2014) 067 [arXiv:1402.4478] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  35. [35]
    A. Gallerati, H. Samtleben and M. Trigiante, The \( \mathcal{N} \) > 2 supersymmetric AdS vacua in maximal supergravity, JHEP 12 (2014) 174 [arXiv:1410.0711] [INSPIRE].ADSCrossRefGoogle Scholar
  36. [36]
    R. Emparan, C.V. Johnson and R.C. Myers, Surface terms as counterterms in the AdS/CFT correspondence, Phys. Rev. D 60 (1999) 104001 [hep-th/9903238] [INSPIRE].ADSMathSciNetGoogle Scholar
  37. [37]
    V. Balasubramanian, P. Kraus and A.E. Lawrence, Bulk versus boundary dynamics in anti-de Sitter space-time, Phys. Rev. D 59 (1999) 046003 [hep-th/9805171] [INSPIRE].ADSMathSciNetGoogle Scholar
  38. [38]
    V. Balasubramanian, P. Kraus, A.E. Lawrence and S.P. Trivedi, Holographic probes of anti-de Sitter space-times, Phys. Rev. D 59 (1999) 104021 [hep-th/9808017] [INSPIRE].ADSMathSciNetGoogle Scholar
  39. [39]
    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].ADSMathSciNetCrossRefGoogle Scholar
  40. [40]
    E. Witten, Anti-de Sitter space and holography, Adv. Theor. Math. Phys. 2 (1998) 253 [hep-th/9802150] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  41. [41]
    H. Lü, Y. Pang and C.N. Pope, AdS Dyonic Black Hole and its Thermodynamics, JHEP 11 (2013) 033 [arXiv:1307.6243] [INSPIRE].MathSciNetCrossRefGoogle Scholar
  42. [42]
    H. Lü, C.N. Pope and Q. Wen, Thermodynamics of AdS Black Holes in Einstein-Scalar Gravity, JHEP 03 (2015) 165 [arXiv:1408.1514] [INSPIRE].MathSciNetCrossRefGoogle Scholar
  43. [43]
    S.S. Gubser, I.R. Klebanov and A.A. Tseytlin, String theory and classical absorption by three-branes, Nucl. Phys. B 499 (1997) 217 [hep-th/9703040] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  44. [44]
    S.S. Gubser and I.R. Klebanov, Absorption by branes and Schwinger terms in the world volume theory, Phys. Lett. B 413 (1997) 41 [hep-th/9708005] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  45. [45]
    R.C. Myers, Stress tensors and Casimir energies in the AdS/CFT correspondence, Phys. Rev. D 60 (1999) 046002 [hep-th/9903203] [INSPIRE].ADSMathSciNetGoogle Scholar
  46. [46]
    S. Hollands, A. Ishibashi and D. Marolf, Comparison between various notions of conserved charges in asymptotically AdS-spacetimes, Class. Quant. Grav. 22 (2005) 2881 [hep-th/0503045] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  47. [47]
    T. Regge and C. Teitelboim, Role of Surface Integrals in the Hamiltonian Formulation of General Relativity, Annals Phys. 88 (1974) 286 [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  48. [48]
    M. Bañados and S. Theisen, Scale invariant hairy black holes, Phys. Rev. D 72 (2005) 064019 [hep-th/0506025] [INSPIRE].ADSGoogle Scholar
  49. [49]
    J. Gegenberg, C. Martínez 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].ADSMathSciNetGoogle Scholar
  50. [50]
    C. Martínez, 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].ADSMathSciNetGoogle Scholar
  51. [51]
    A. Anabalón, Exact Black Holes and Universality in the Backreaction of non-linear σ-models with a potential in (A)dS4, JHEP 06 (2012) 127 [arXiv:1204.2720] [INSPIRE].ADSCrossRefGoogle Scholar
  52. [52]
    A. Guarino, On new maximal supergravity and its BPS domain-walls, JHEP 02 (2014) 026 [arXiv:1311.0785] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  53. [53]
    A. Anabalón, D. Astefanesei and R. Mann, Exact asymptotically flat charged hairy black holes with a dilaton potential, JHEP 10 (2013) 184 [arXiv:1308.1693] [INSPIRE].ADSCrossRefGoogle Scholar
  54. [54]
    T. Hertog and G.T. Horowitz, Towards a big crunch dual, JHEP 07 (2004) 073 [hep-th/0406134] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  55. [55]
    S. de Haro, S.N. Solodukhin and K. Skenderis, Holographic reconstruction of space-time and renormalization in the AdS/CFT correspondence, Commun. Math. Phys. 217 (2001) 595 [hep-th/0002230] [INSPIRE].ADSCrossRefMATHGoogle Scholar
  56. [56]
    M. Bianchi, D.Z. Freedman and K. Skenderis, Holographic renormalization, Nucl. Phys. B 631 (2002) 159 [hep-th/0112119] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  57. [57]
    R.B. Mann and D. Marolf, Holographic renormalization of asymptotically flat spacetimes, Class. Quant. Grav. 23 (2006) 2927 [hep-th/0511096] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  58. [58]
    D. Astefanesei and E. Radu, Quasilocal formalism and black ring thermodynamics, Phys. Rev. D 73 (2006) 044014 [hep-th/0509144] [INSPIRE].ADSMathSciNetGoogle Scholar
  59. [59]
    R.B. Mann, D. Marolf and A. Virmani, Covariant Counterterms and Conserved Charges in Asymptotically Flat Spacetimes, Class. Quant. Grav. 23 (2006) 6357 [gr-qc/0607041] [INSPIRE].
  60. [60]
    D. Astefanesei, R.B. Mann and C. Stelea, Note on counterterms in asymptotically flat spacetimes, Phys. Rev. D 75 (2007) 024007 [hep-th/0608037] [INSPIRE].ADSMathSciNetGoogle Scholar
  61. [61]
    D. Marolf, Asymptotic flatness, little string theory and holography, JHEP 03 (2007) 122 [hep-th/0612012] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  62. [62]
    D. Astefanesei, M.J. Rodriguez and S. Theisen, Quasilocal equilibrium condition for black ring, JHEP 12 (2009) 040 [arXiv:0909.0008] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  63. [63]
    D. Astefanesei, R.B. Mann, M.J. Rodriguez and C. Stelea, Quasilocal formalism and thermodynamics of asymptotically flat black objects, Class. Quant. Grav. 27 (2010) 165004 [arXiv:0909.3852] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  64. [64]
    D. Astefanesei, M.J. Rodriguez and S. Theisen, Thermodynamic instability of doubly spinning black objects, JHEP 08 (2010) 046 [arXiv:1003.2421] [INSPIRE].ADSCrossRefMATHGoogle Scholar
  65. [65]
    V. Balasubramanian, J. de Boer and D. Minic, Mass, entropy and holography in asymptotically de Sitter spaces, Phys. Rev. D 65 (2002) 123508 [hep-th/0110108] [INSPIRE].ADSMathSciNetGoogle Scholar
  66. [66]
    A.M. Ghezelbash and R.B. Mann, Action, mass and entropy of Schwarzschild-de Sitter black holes and the de Sitter/CFT correspondence, JHEP 01 (2002) 005 [hep-th/0111217] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  67. [67]
    A.M. Ghezelbash, D. Ida, R.B. Mann and T. Shiromizu, Slicing and brane dependence of the (A)dS/CFT correspondence, Phys. Lett. B 535 (2002) 315 [hep-th/0201004] [INSPIRE].ADSCrossRefMATHGoogle Scholar
  68. [68]
    D. Astefanesei, R.B. Mann and E. Radu, Reissner-Nordstrom-de Sitter black hole, planar coordinates and dS/CFT, JHEP 01 (2004) 029 [hep-th/0310273] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  69. [69]
    A. Sen, Entropy function for heterotic black holes, JHEP 03 (2006) 008 [hep-th/0508042] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  70. [70]
    A. Sen, Black hole entropy function and the attractor mechanism in higher derivative gravity, JHEP 09 (2005) 038 [hep-th/0506177] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  71. [71]
    A. Sen, Black Hole Entropy Function, Attractors and Precision Counting of Microstates, Gen. Rel. Grav. 40 (2008) 2249 [arXiv:0708.1270] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  72. [72]
    D. Astefanesei, K. Goldstein, R.P. Jena, A. Sen and S.P. Trivedi, Rotating attractors, JHEP 10 (2006) 058 [hep-th/0606244] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  73. [73]
    D. Astefanesei, N. Banerjee and S. Dutta, (Un)attractor black holes in higher derivative AdS gravity, JHEP 11 (2008) 070 [arXiv:0806.1334] [INSPIRE].
  74. [74]
    D. Astefanesei, H. Nastase, H. Yavartanoo and S. Yun, Moduli flow and non-supersymmetric AdS attractors, JHEP 04 (2008) 074 [arXiv:0711.0036] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  75. [75]
    J.F. Morales and H. Samtleben, Entropy function and attractors for AdS black holes, JHEP 10 (2006) 074 [hep-th/0608044] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  76. [76]
    D. Astefanesei, N. Banerjee and S. Dutta, Moduli and electromagnetic black brane holography, JHEP 02 (2011) 021 [arXiv:1008.3852] [INSPIRE].ADSMathSciNetMATHGoogle Scholar
  77. [77]
    D. Astefanesei, N. Banerjee and S. Dutta, Near horizon data and physical charges of extremal AdS black holes, Nucl. Phys. B 853 (2011) 63 [arXiv:1104.4121] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  78. [78]
    A. Anabalón, D. Astefanesei and D. Choque, On the thermodynamics of hairy black holes, Phys. Lett. B 743 (2015) 154 [arXiv:1501.04252] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  79. [79]
    A. Anabalón, D. Astefanesei and D. Choque, in preparation.Google Scholar
  80. [80]
    J.D. Bekenstein, Transcendence of the law of baryon-number conservation in black hole physics, Phys. Rev. Lett. 28 (1972) 452 [INSPIRE].ADSCrossRefGoogle Scholar
  81. [81]
    J.D. Bekenstein, Nonexistence of baryon number for black holes. II, Phys. Rev. D 5 (1972) 2403 [INSPIRE].
  82. [82]
    M. Heusler, A No hair theorem for selfgravitating nonlinear σ-models, J. Math. Phys. 33 (1992) 3497 [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  83. [83]
    D. Sudarsky, A Simple proof of a no hair theorem in Einstein Higgs theory, Class. Quant. Grav. 12 (1995) 579 [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  84. [84]
    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].ADSMathSciNetCrossRefGoogle Scholar
  85. [85]
    T. Torii, K. Maeda and M. Narita, Scalar hair on the black hole in asymptotically anti-de Sitter space-time, Phys. Rev. D 64 (2001) 044007 [INSPIRE].ADSMathSciNetGoogle Scholar
  86. [86]
    D. Sudarsky and J.A. Gonzalez, On black hole scalar hair in asymptotically anti-de Sitter space-times, Phys. Rev. D 67 (2003) 024038 [gr-qc/0207069] [INSPIRE].
  87. [87]
    T. Kolyvaris, G. Koutsoumbas, E. Papantonopoulos and G. Siopsis, A New Class of Exact Hairy Black Hole Solutions, Gen. Rel. Grav. 43 (2011) 163 [arXiv:0911.1711] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  88. [88]
    A. Anabalón, F. Canfora, A. Giacomini and J. Oliva, Black Holes with Primary Hair in gauged N = 8 Supergravity, JHEP 06 (2012) 010 [arXiv:1203.6627] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  89. [89]
    P.A. González, E. Papantonopoulos, J. Saavedra and Y. Vásquez, Four-Dimensional Asymptotically AdS Black Holes with Scalar Hair, JHEP 12 (2013) 021 [arXiv:1309.2161] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  90. [90]
    X.-H. Feng, H. Lü and Q. Wen, Scalar Hairy Black Holes in General Dimensions, Phys. Rev. D 89 (2014) 044014 [arXiv:1312.5374] [INSPIRE].ADSGoogle Scholar
  91. [91]
    A. Anabalón, D. Astefanesei and J. Oliva, Hairy Black Hole Stability in AdS, Quantum Mechanics on the Half-Line and Holography, JHEP 10 (2015) 068 [arXiv:1507.05520] [INSPIRE].ADSCrossRefGoogle Scholar
  92. [92]
    D. Astefanesei and E. Radu, Boson stars with negative cosmological constant, Nucl. Phys. B 665 (2003) 594 [gr-qc/0309131] [INSPIRE].
  93. [93]
    P. Bizon and A. Rostworowski, On weakly turbulent instability of anti-de Sitter space, Phys. Rev. Lett. 107 (2011) 031102 [arXiv:1104.3702] [INSPIRE].ADSCrossRefGoogle Scholar
  94. [94]
    A. Buchel, S.L. Liebling and L. Lehner, Boson stars in AdS spacetime, Phys. Rev. D 87 (2013) 123006 [arXiv:1304.4166] [INSPIRE].ADSGoogle Scholar
  95. [95]
    D. Astefanesei and E. Radu, Rotating boson stars in (2+1)-dimenmsions, Phys. Lett. B 587 (2004) 7 [gr-qc/0310135] [INSPIRE].
  96. [96]
    A. Buchel, AdS boson stars in string theory, arXiv:1510.08415 [INSPIRE].

Copyright information

© The Author(s) 2016

Authors and Affiliations

  • Andrés Anabalón
    • 1
  • Dumitru Astefanesei
    • 2
    • 3
  • David Choque
    • 3
    • 4
  • Cristián Martínez
    • 5
  1. 1.Departamento de Ciencias, Facultad de Artes Liberales and Facultad de Ingeniería y CienciasUniversidad Adolfo IbáñezViña del MarChile
  2. 2.Instituto de FísicaPontificia Universidad Católica de ValparaísoValparaísoChile
  3. 3.Max-Planck-Institut für Gravitationsphysik, Albert-Einstein-InstitutGolmGermany
  4. 4.Universidad Técnica Federico Santa MaríaValparaísoChile
  5. 5.Centro de Estudios Científicos (CECs)ValdiviaChile

Personalised recommendations