Advertisement

Journal of High Energy Physics

, 2019:142 | Cite as

Charged scalar-tensor solitons and black holes with (approximate) Anti-de Sitter asymptotics

  • Yves Brihaye
  • Betti HartmannEmail author
Open Access
Regular Article - Theoretical Physics
  • 18 Downloads

Abstract

We discuss charged and static solutions in a shift-symmetric scalar-tensor gravity model including a negative cosmological constant. The solutions are only approximately Anti-de Sitter (AdS) asymptotically. While spherically symmetric black holes with scalar-tensor hair do exist in our model, the uncharged spherically symmetric scalar-tensor solitons constructed recently cannot be generalised to include charge. We point out that this is due to the divergence of the electric monopole at the origin of the coordinate system, while higher order multipoles are well-behaved. We also demonstrate that black holes with scalar hair exist only for horizon value larger than that of the corresponding extremal Reissner-Nordström-AdS (RNAdS) solution, i.e. that we cannot construct solutions with arbitrarily small horizon radius. We demonstrate that for fixed Q a horizon radius exists at which the specific heat CQ diverges — signalling a transition from thermodynamically unstable to stable black holes. In contrast to the RNAdS case, however, we have only been able to construct a stable phase of large horizon black holes, while a stable phase of small horizon black holes does not (seem to) exist.

Keywords

Black Holes Classical Theories of Gravity 

Notes

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.

References

  1. [1]
    K. Schwarzschild, On the gravitational field of a mass point according to Einstein’s theory, Sitzungsber. Preuss. Akad. Wiss. Berlin 1916 (1916) 189 [physics/9905030] [INSPIRE].
  2. [2]
    R. Penrose, Gravitational collapse and space-time singularities, Phys. Rev. Lett. 14 (1965) 57 [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  3. [3]
    P.T. Chrusciel, ‘No hair’ theorems: Folklore, conjectures, results, Contemp. Math. 170 (1994) 23 [gr-qc/9402032] [INSPIRE].
  4. [4]
    M. Heusler, Stationary black holes: Uniqueness and beyond, Living Rev. Rel. 1 (1998) 6 [INSPIRE].MathSciNetCrossRefzbMATHGoogle Scholar
  5. [5]
    J.D. Bekenstein, Black holes: Classical properties, thermodynamics and heuristic quantization, in proceedings of the 9th Brazilian School of Cosmology and Gravitation (BSCG 1998), Rio de Janeiro, Brazil, 27 July–7 August 1998, gr-qc/9808028 [INSPIRE].
  6. [6]
    D.C. Robinson, Four decades of black hole uniqueness theorems, in The Kerr Spacetime: Rotating Black Holes in General Relativity, D.L. Wiltshire, M. Visser and S.M. Scott eds., Cambridge University Press (2009).Google Scholar
  7. [7]
    H. Lückock and I. Moss, Black Holes Have Skyrmion Hair, Phys. Lett. B 176 (1986) 341 [INSPIRE].ADSCrossRefGoogle Scholar
  8. [8]
    K.-M. Lee, V.P. Nair and E.J. Weinberg, Black holes in magnetic monopoles, Phys. Rev. D 45 (1992) 2751 [hep-th/9112008] [INSPIRE].ADSMathSciNetzbMATHGoogle Scholar
  9. [9]
    P. Breitenlohner, P. Forgacs and D. Maison, Gravitating monopole solutions, Nucl. Phys. B 383 (1992) 357 [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  10. [10]
    P. Breitenlohner, P. Forgacs and D. Maison, Gravitating monopole solutions. 2, Nucl. Phys. B 442 (1995) 126 [gr-qc/9412039] [INSPIRE].
  11. [11]
    P.C. Aichelburg and P. Bizon, Magnetically charged black holes and their stability, Phys. Rev. D 48 (1993) 607 [gr-qc/9212009] [INSPIRE].
  12. [12]
    S.S. Gubser, Breaking an Abelian gauge symmetry near a black hole horizon, Phys. Rev. D 78 (2008) 065034 [arXiv:0801.2977] [INSPIRE].ADSGoogle Scholar
  13. [13]
    J.M. Bardeen, B. Carter and S.W. Hawking, The Four laws of black hole mechanics, Commun. Math. Phys. 31 (1973) 161 [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  14. [14]
    S.W. Hawking, Black hole explosions, Nature 248 (1974) 30 [INSPIRE].ADSCrossRefzbMATHGoogle Scholar
  15. [15]
    LIGO Scientific and Virgo collaborations, Observation of Gravitational Waves from a Binary Black Hole Merger, Phys. Rev. Lett. 116 (2016) 061102 [arXiv:1602.03837] [INSPIRE].
  16. [16]
    LIGO Scientific and Virgo collaborations, GW151226: Observation of Gravitational Waves from a 22-Solar-Mass Binary Black Hole Coalescence, Phys. Rev. Lett. 116 (2016) 241103 [arXiv:1606.04855] [INSPIRE].
  17. [17]
    LIGO Scientific and VIRGO collaborations, GW170104: Observation of a 50-Solar-Mass Binary Black Hole Coalescence at Redshift 0.2, Phys. Rev. Lett. 118 (2017) 221101 [Erratum ibid. 121 (2018) 129901] [arXiv:1706.01812] [INSPIRE].
  18. [18]
    LIGO Scientific and Virgo collaborations, GW170814: A Three-Detector Observation of Gravitational Waves from a Binary Black Hole Coalescence, Phys. Rev. Lett. 119 (2017) 141101 [arXiv:1709.09660] [INSPIRE].
  19. [19]
    LIGO Scientific and Virgo collaborations, GW170608: Observation of a 19-Solar-mass Binary Black Hole Coalescence, Astrophys. J. 851 (2017) L35 [arXiv:1711.05578] [INSPIRE].
  20. [20]
    LIGO Scientific, Virgo, Fermi-GBM and INTEGRAL collaborations, Gravitational Waves and Gamma-rays from a Binary Neutron Star Merger: GW170817 and GRB 170817A, Astrophys. J. 848 (2017) L13 [arXiv:1710.05834] [INSPIRE].
  21. [21]
    LIGO Scientific and Virgo collaborations, GW170817: Observation of Gravitational Waves from a Binary Neutron Star Inspiral, Phys. Rev. Lett. 119 (2017) 161101 [arXiv:1710.05832] [INSPIRE].
  22. [22]
    E. Troja et al., The X-ray counterpart to the gravitational wave event GW 170817, Nature 551 (2017) 71 [arXiv:1710.05433] [INSPIRE].ADSCrossRefGoogle Scholar
  23. [23]
    J.M. Maldacena, The Large N limit of superconformal field theories and supergravity, Int. J. Theor. Phys. 38 (1999) 1113 [Adv. Theor. Math. Phys. 2 (1998) 231] [hep-th/9711200] [INSPIRE].
  24. [24]
    O. Aharony, S.S. Gubser, J.M. Maldacena, H. Ooguri and Y. Oz, Large N field theories, string theory and gravity, Phys. Rept. 323 (2000) 183 [hep-th/9905111] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  25. [25]
    E. D’Hoker and D.Z. Freedman, Supersymmetric gauge theories and the AdS/CFT correspondence, in proceedings of the Theoretical Advanced Study Institute in Elementary Particle Physics (TASI 2001): Strings, Branes and EXTRA Dimensions, Boulder, Colorado, U.S.A., 3–29 June 2001, pp. 3–158 [hep-th/0201253] [INSPIRE].
  26. [26]
    M.K. Benna and I.R. Klebanov, Course 13. Gauge-String Dualities and Some Applications, Les Houches 87 (2008) 611 [arXiv:0803.1315] [INSPIRE].
  27. [27]
    S.A. Hartnoll, C.P. Herzog and G.T. Horowitz, Holographic Superconductors, JHEP 12 (2008) 015 [arXiv:0810.1563] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  28. [28]
    S.A. Hartnoll, C.P. Herzog and G.T. Horowitz, Building a Holographic Superconductor, Phys. Rev. Lett. 101 (2008) 031601 [arXiv:0803.3295] [INSPIRE].ADSCrossRefzbMATHGoogle Scholar
  29. [29]
    C.P. Herzog, Lectures on Holographic Superfluidity and Superconductivity, J. Phys. A 42 (2009) 343001 [arXiv:0904.1975] [INSPIRE].MathSciNetzbMATHGoogle Scholar
  30. [30]
    S.A. Hartnoll, Lectures on holographic methods for condensed matter physics, Class. Quant. Grav. 26 (2009) 224002 [arXiv:0903.3246] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  31. [31]
    G.T. Horowitz, Introduction to Holographic Superconductors, Lect. Notes Phys. 828 (2011) 313 [arXiv:1002.1722] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  32. [32]
    S.A. Hartnoll, Horizons, holography and condensed matter, in Black holes in higher dimensions, G.T. Horowitz ed., Cambridge University Press (2012), pp. 387–419 [arXiv:1106.4324] [INSPIRE].
  33. [33]
    M. Ammon and J. Erdmenger, Gauge/gravity duality: Foundations and applications, Cambridge University Press (2015).Google Scholar
  34. [34]
    A. Chamblin, R. Emparan, C.V. Johnson and R.C. Myers, Charged AdS black holes and catastrophic holography, Phys. Rev. D 60 (1999) 064018 [hep-th/9902170] [INSPIRE].ADSMathSciNetGoogle Scholar
  35. [35]
    A. Chamblin, R. Emparan, C.V. Johnson and R.C. Myers, Holography, thermodynamics and fluctuations of charged AdS black holes, Phys. Rev. D 60 (1999) 104026 [hep-th/9904197] [INSPIRE].ADSMathSciNetGoogle Scholar
  36. [36]
    X.N. Wu, Multicritical phenomena of Reissner-Nordstrom anti-de Sitter black holes, Phys. Rev. D 62 (2000) 124023 [INSPIRE].ADSGoogle Scholar
  37. [37]
    D. Kubiznak and R.B. Mann, Black hole chemistry, Can. J. Phys. 93 (2015) 999 [arXiv:1404.2126] [INSPIRE].ADSCrossRefGoogle Scholar
  38. [38]
    R.B. Mann, The Chemistry of Black Holes, Springer Proc. Phys. 170 (2016) 197 [INSPIRE].CrossRefGoogle Scholar
  39. [39]
    D. Kubiznak, R.B. Mann and M. Teo, Black hole chemistry: thermodynamics with Lambda, Class. Quant. Grav. 34 (2017) 063001 [arXiv:1608.06147] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  40. [40]
    C. Deffayet and D.A. Steer, A formal introduction to Horndeski and Galileon theories and their generalizations, Class. Quant. Grav. 30 (2013) 214006 [arXiv:1307.2450] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  41. [41]
    C. Charmousis, From Lovelock to Horndeski’s Generalized Scalar Tensor Theory, Lect. Notes Phys. 892 (2015) 25 [arXiv:1405.1612] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  42. [42]
    G.W. Horndeski, Second-order scalar-tensor field equations in a four-dimensional space, Int. J. Theor. Phys. 10 (1974) 363 [INSPIRE].MathSciNetCrossRefGoogle Scholar
  43. [43]
    E. Babichev, C. Charmousis and A. Lehébel, Asymptotically flat black holes in Horndeski theory and beyond, JCAP 04 (2017) 027 [arXiv:1702.01938] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  44. [44]
    T.P. Sotiriou and S.-Y. Zhou, Black hole hair in generalized scalar-tensor gravity: An explicit example, Phys. Rev. D 90 (2014) 124063 [arXiv:1408.1698] [INSPIRE].ADSGoogle Scholar
  45. [45]
    J.M. Ezquiaga and M. Zumalacárregui, Dark Energy After GW170817: Dead Ends and the Road Ahead, Phys. Rev. Lett. 119 (2017) 251304 [arXiv:1710.05901] [INSPIRE].ADSCrossRefGoogle Scholar
  46. [46]
    Y. Brihaye, B. Hartmann and J. Urrestilla, Solitons and black hole in shift symmetric scalar-tensor gravity with cosmological constant, JHEP 06 (2018) 074 [arXiv:1712.02458] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  47. [47]
    C.A.R. 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].ADSCrossRefzbMATHGoogle Scholar
  48. [48]
    U. Ascher, J. Christiansen and R.D. Russell, A Collocation Solver for Mixed Order Systems of Boundary Value Problems, Math. Comput. 33 (1979) 659 [INSPIRE].MathSciNetCrossRefzbMATHGoogle Scholar
  49. [49]
    U. Ascher, J. Christiansen and R.D. Russell, Collocation software for boundary-value ODEs, ACM Trans. Math. Software 7 (1981) 209.CrossRefzbMATHGoogle Scholar
  50. [50]
    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].ADSCrossRefGoogle Scholar
  51. [51]
    Y. Brihaye and L. Ducobu, Hairy black holes: from shift symmetry to spontaneous scalarization, arXiv:1812.07438 [INSPIRE].

Copyright information

© The Author(s) 2019

Authors and Affiliations

  1. 1.Physique-MathématiqueUniversité de Mons-HainautMonsBelgium
  2. 2.Instituto de Física de São Carlos (IFSC)Universidade de São Paulo (USP)São CarlosBrazil

Personalised recommendations