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Charged scalar-tensor solitons and black holes with (approximate) anti-de Sitter asymptotics. (English) Zbl 1409.83087
Summary: 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 $$C_Q$$ 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.

##### MSC:
 83C57 Black holes 83C15 Exact solutions to problems in general relativity and gravitational theory 83D05 Relativistic gravitational theories other than Einstein’s, including asymmetric field theories 83C22 Einstein-Maxwell equations
##### Keywords:
black holes; classical theories of gravity
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##### References:
 [1] K. Schwarzschild, On the gravitational field of a mass point according to Einstein’s theory, Sitzungsber. Preuss. Akad. Wiss. Berlin1916 (1916) 189 [physics/9905030] [INSPIRE]. [2] Penrose, R., Gravitational collapse and space-time singularities, Phys. Rev. Lett., 14, 57, (1965) · Zbl 0125.21206 [3] P.T. Chrusciel, ‘No hair’ theorems: Folklore, conjectures, results, Contemp. Math.170 (1994) 23 [gr-qc/9402032] [INSPIRE]. · Zbl 0864.53068 [4] Heusler, M., Stationary black holes: Uniqueness and beyond, Living Rev. Rel., 1, 6, (1998) · Zbl 1023.83006 [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] 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). [7] Lückock, H.; Moss, I., Black Holes Have Skyrmion Hair, Phys. Lett., B 176, 341, (1986) [8] Lee, K-M; Nair, VP; Weinberg, EJ, Black holes in magnetic monopoles, Phys. Rev., D 45, 2751, (1992) · Zbl 1232.81033 [9] Breitenlohner, P.; Forgacs, P.; Maison, D., Gravitating monopole solutions, Nucl. Phys., B 383, 357, (1992) · Zbl 0990.81574 [10] P. Breitenlohner, P. Forgacs and D. Maison, Gravitating monopole solutions. 2, Nucl. Phys.B 442 (1995) 126 [gr-qc/9412039] [INSPIRE]. · Zbl 0990.81574 [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] Gubser, SS, Breaking an Abelian gauge symmetry near a black hole horizon, Phys. Rev., D 78, (2008) [13] Bardeen, JM; Carter, B.; Hawking, SW, The Four laws of black hole mechanics, Commun. Math. Phys., 31, 161, (1973) · Zbl 1125.83309 [14] Hawking, SW, Black hole explosions, Nature, 248, 30, (1974) · Zbl 1370.83053 [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] 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] 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] 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] 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] 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] 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] Troja, E.; etal., The X-ray counterpart to the gravitational wave event GW 170817, Nature, 551, 71, (2017) [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]. · Zbl 0914.53047 [24] Aharony, O.; Gubser, SS; Maldacena, JM; Ooguri, H.; Oz, Y., Large N field theories, string theory and gravity, Phys. Rept., 323, 183, (2000) · Zbl 1368.81009 [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] M.K. Benna and I.R. Klebanov, Course 13. Gauge-String Dualities and Some Applications, Les Houches87 (2008) 611 [arXiv:0803.1315] [INSPIRE]. [27] Hartnoll, SA; Herzog, CP; Horowitz, GT, Holographic Superconductors, JHEP, 12, 015, (2008) · Zbl 1329.81390 [28] Hartnoll, SA; Herzog, CP; Horowitz, GT, Building a Holographic Superconductor, Phys. Rev. Lett., 101, (2008) · Zbl 1404.82086 [29] Herzog, CP, Lectures on Holographic Superfluidity and Superconductivity, J. Phys., A 42, 343001, (2009) · Zbl 1180.82218 [30] Hartnoll, SA, Lectures on holographic methods for condensed matter physics, Class. Quant. Grav., 26, 224002, (2009) · Zbl 1181.83003 [31] Horowitz, GT, Introduction to Holographic Superconductors, Lect. Notes Phys., 828, 313, (2011) · Zbl 1246.83009 [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]. · Zbl 1269.83006 [33] M. Ammon and J. Erdmenger, Gauge/gravity duality: Foundations and applications, Cambridge University Press (2015). · Zbl 1327.81001 [34] Chamblin, A.; Emparan, R.; Johnson, CV; Myers, RC, Charged AdS black holes and catastrophic holography, Phys. Rev., D 60, (1999) [35] Chamblin, A.; Emparan, R.; Johnson, CV; Myers, RC, Holography, thermodynamics and fluctuations of charged AdS black holes, Phys. Rev., D 60, 104026, (1999) [36] Wu, XN, Multicritical phenomena of Reissner-Nordstrom anti-de Sitter black holes, Phys. Rev., D 62, 124023, (2000) [37] Kubiznak, D.; Mann, RB, Black hole chemistry, Can. J. Phys., 93, 999, (2015) [38] Mann, RB, The Chemistry of Black Holes, Springer Proc. Phys., 170, 197, (2016) [39] Kubiznak, D.; Mann, RB; Teo, M., Black hole chemistry: thermodynamics with Lambda, Class. Quant. Grav., 34, (2017) · Zbl 1368.83002 [40] Deffayet, C.; Steer, DA, A formal introduction to Horndeski and Galileon theories and their generalizations, Class. Quant. Grav., 30, 214006, (2013) · Zbl 1277.83006 [41] Charmousis, C., From Lovelock to Horndeski’s Generalized Scalar Tensor Theory, Lect. Notes Phys., 892, 25, (2015) [42] Horndeski, GW, Second-order scalar-tensor field equations in a four-dimensional space, Int. J. Theor. Phys., 10, 363, (1974) [43] Babichev, E.; Charmousis, C.; Lehébel, A., Asymptotically flat black holes in Horndeski theory and beyond, JCAP, 04, 027, (2017) · Zbl 1346.83035 [44] Sotiriou, TP; Zhou, S-Y, Black hole hair in generalized scalar-tensor gravity: An explicit example, Phys. Rev., D 90, 124063, (2014) [45] Ezquiaga, JM; Zumalacárregui, M., Dark Energy After GW170817: Dead Ends and the Road Ahead, Phys. Rev. Lett., 119, 251304, (2017) [46] Brihaye, Y.; Hartmann, B.; Urrestilla, J., Solitons and black hole in shift symmetric scalar-tensor gravity with cosmological constant, JHEP, 06, 074, (2018) · Zbl 1395.83040 [47] Herdeiro, CAR; Radu, E., Anti-de-Sitter regular electric multipoles: Towards Einstein-Maxwell-AdS solitons, Phys. Lett., B 749, 393, (2015) · Zbl 1364.83034 [48] Ascher, U.; Christiansen, J.; Russell, RD, A Collocation Solver for Mixed Order Systems of Boundary Value Problems, Math. Comput., 33, 659, (1979) · Zbl 0407.65035 [49] Ascher, U.; Christiansen, J.; Russell, RD, Collocation software for boundary-value ODEs, ACM Trans. Math. Software, 7, 209, (1981) · Zbl 0455.65067 [50] Herdeiro, CAR; Radu, E., Static Einstein-Maxwell black holes with no spatial isometries in AdS space, Phys. Rev. Lett., 117, 221102, (2016) [51] Y. Brihaye and L. Ducobu, Hairy black holes: from shift symmetry to spontaneous scalarization, arXiv:1812.07438 [INSPIRE]. · Zbl 1344.83027
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