Abstract
We consider a gravitating system consisting of a scalar field minimally coupled to gravity with a self-interacting potential and an U(1) electromagnetic field. Solving the coupled Einstein-Maxwell-scalar system we find exact hairy charged black hole solutions with the scalar field regular everywhere. We go to the zero temperature limit and we study the effect of the scalar field on the near horizon geometry of an extremal black hole. We find that except a critical value of the charge of the black hole there is also a critical value of the charge of the scalar field beyond of which the extremal black hole is destabilized. We study the thermodynamics of these solutions and we find that if the space is flat then the Reissner-Nordström black hole is thermodynamically preferred, while if the space is AdS the hairy charged black hole is thermodynamically preferred at low temperature.
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References
J.M. Maldacena, The large-N limit of superconformal field theories and supergravity, Int. J. Theor. Phys. 38 (1999) 1113 [hep-th/9711200] [INSPIRE].
H. Liu, J. McGreevy and D. Vegh, Non-Fermi liquids from holography, Phys. Rev. D 83 (2011) 065029 [arXiv:0903.2477] [INSPIRE].
T. Faulkner, H. Liu, J. McGreevy and D. Vegh, Emergent quantum criticality, Fermi surfaces and AdS 2, Phys. Rev. D 83 (2011) 125002 [arXiv:0907.2694] [INSPIRE].
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].
H.K. Kunduri and J. Lucietti, Classification of near-horizon geometries of extremal black holes, Living Rev. Rel. 16 (2013) 8 [arXiv:1306.2517] [INSPIRE].
G.T. Horowitz and M.M. Roberts, Zero Temperature Limit of Holographic Superconductors, JHEP 11 (2009) 015 [arXiv:0908.3677] [INSPIRE].
J. Alsup, G. Siopsis and J. Therrien, Hair on near-extremal Reissner-Nordstrom AdS black holes, Phys. Rev. D 86 (2012) 025002 [arXiv:1110.3342] [INSPIRE].
J. Fernandez-Gracia and B. Fiol, A no-hair theorem for extremal black branes, JHEP 11 (2009) 054 [arXiv:0906.2353] [INSPIRE].
D.-f. Zeng, An Exact Hairy Black Hole Solution for AdS/CFT Superconductors, arXiv:0903.2620 [INSPIRE].
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].
N. Bocharova, K. Bronnikov and V. Melnikov, The first MP-type solution with a conformal scalar field, Moscow Univ. Phys. Bull. 25 (1970) 80 [Vestn. Mosk. Univ. Fiz. Astron. 6 (1970) 706].
J.D. Bekenstein, Exact solutions of Einstein conformal scalar equations, Annals Phys. 82 (1974) 535 [INSPIRE].
J.D. Bekenstein, Black Holes with Scalar Charge, Annals Phys. 91 (1975) 75 [INSPIRE].
K.A. Bronnikov and Y. Kireev, Instability of Black Holes with Scalar Charge, Phys. Lett. A 67 (1978) 95 [INSPIRE].
K.G. Zloshchastiev, On co-existence of black holes and scalar field, Phys. Rev. Lett. 94 (2005) 121101 [hep-th/0408163] [INSPIRE].
C. Martinez, R. Troncoso and J. Zanelli, de Sitter black hole with a conformally coupled scalar field in four-dimensions, Phys. Rev. D 67 (2003) 024008 [hep-th/0205319] [INSPIRE].
G. Dotti, R.J. Gleiser and C. Martinez, Static black hole solutions with a self interacting conformally coupled scalar field, Phys. Rev. D 77 (2008) 104035 [arXiv:0710.1735] [INSPIRE].
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].
E. Winstanley, On the existence of conformally coupled scalar field hair for black holes in (anti-)de Sitter space, Found. Phys. 33 (2003) 111 [gr-qc/0205092] [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].
C. Martinez, J.P. Staforelli and R. Troncoso, Topological black holes dressed with a conformally coupled scalar field and electric charge, Phys. Rev. D 74 (2006) 044028 [hep-th/0512022] [INSPIRE].
G. Koutsoumbas, S. Musiri, E. Papantonopoulos and G. Siopsis, Quasi-normal Modes of Electromagnetic Perturbations of Four-Dimensional Topological Black Holes with Scalar Hair, JHEP 10 (2006) 006 [hep-th/0606096] [INSPIRE].
C. Martinez and A. Montecinos, Phase transitions in charged topological black holes dressed with a scalar hair, Phys. Rev. D 82 (2010) 127501 [arXiv:1009.5681] [INSPIRE].
C. Martinez and R. Troncoso, Electrically charged black hole with scalar hair, Phys. Rev. D 74 (2006) 064007 [hep-th/0606130] [INSPIRE].
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].
C. Charmousis, T. Kolyvaris and E. Papantonopoulos, Charged C-metric with conformally coupled scalar field, Class. Quant. Grav. 26 (2009) 175012 [arXiv:0906.5568] [INSPIRE].
A. Anabalon, 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].
A. Anabalon and J. Oliva, Exact Hairy Black Holes and their Modification to the Universal Law of Gravitation, Phys. Rev. D 86 (2012) 107501 [arXiv:1205.6012] [INSPIRE].
Y. Bardoux, M.M. Caldarelli and C. Charmousis, Conformally coupled scalar black holes admit a flat horizon due to axionic charge, JHEP 09 (2012) 008 [arXiv:1205.4025] [INSPIRE].
T. Kolyvaris, G. Koutsoumbas, E. Papantonopoulos and G. Siopsis, Scalar Hair from a Derivative Coupling of a Scalar Field to the Einstein Tensor, Class. Quant. Grav. 29 (2012) 205011 [arXiv:1111.0263] [INSPIRE].
T. Kolyvaris, G. Koutsoumbas, E. Papantonopoulos and G. Siopsis, Phase Transition to a Hairy Black Hole in Asymptotically Flat Spacetime, JHEP 11 (2013) 133 [arXiv:1308.5280] [INSPIRE].
A. Anabalon, D. Astefanesei and R. Mann, Exact asymptotically flat charged hairy black holes with a dilaton potential, JHEP 10 (2013) 184 [arXiv:1308.1693] [INSPIRE].
A. Anabalon and D. Astefanesei, On attractor mechanism of AdS 4 black holes, Phys. Lett. B 727 (2013) 568 [arXiv:1309.5863] [INSPIRE].
C. Charmousis, T. Kolyvaris, E. Papantonopoulos and M. Tsoukalas, Black Holes in Bi-scalar Extensions of Horndeski Theories, JHEP 07 (2014) 085 [arXiv:1404.1024] [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].
S. Stotyn, M. Park, P. McGrath and R.B. Mann, Black Holes and Boson Stars with One Killing Field in Arbitrary Odd Dimensions, Phys. Rev. D 85 (2012) 044036 [arXiv:1110.2223] [INSPIRE].
O.J.C. Dias et al., Hairy black holes and solitons in global AdS 5, JHEP 08 (2012) 117 [arXiv:1112.4447] [INSPIRE].
B. Kleihaus, J. Kunz, E. Radu and B. Subagyo, Axially symmetric static scalar solitons and black holes with scalar hair, Phys. Lett. B 725 (2013) 489 [arXiv:1306.4616] [INSPIRE].
C.A.R. Herdeiro and E. Radu, Kerr black holes with scalar hair, Phys. Rev. Lett. 112 (2014) 221101 [arXiv:1403.2757] [INSPIRE].
C.A.R. Herdeiro and E. Radu, A new spin on black hole hair, arXiv:1405.3696 [INSPIRE].
H. Lü, C.N. Pope and Q. Wen, Thermodynamics of AdS Black Holes in Einstein-Scalar Gravity, arXiv:1408.1514 [INSPIRE].
P. Breitenlohner and D.Z. Freedman, Stability in Gauged Extended Supergravity, Annals Phys. 144 (1982) 249 [INSPIRE].
B.C. Xanthopoulos and T. Zannias, Einstein Gravity Coupled to a Massless Scalar Field in Arbitrary Space-time Dimensions, Phys. Rev. D 40 (1989) 2564 [INSPIRE].
L. Amendola, Cosmology with nonminimal derivative couplings, Phys. Lett. B 301 (1993) 175 [gr-qc/9302010] [INSPIRE].
S.V. Sushkov, Exact cosmological solutions with nonminimal derivative coupling, Phys. Rev. D 80 (2009) 103505 [arXiv:0910.0980] [INSPIRE].
A. Anabalon, A. Cisterna and J. Oliva, Asymptotically locally AdS and flat black holes in Horndeski theory, Phys. Rev. D 89 (2014) 084050 [arXiv:1312.3597] [INSPIRE].
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González, P.A., Papantonopoulos, E., Saavedra, J. et al. Extremal hairy black holes. J. High Energ. Phys. 2014, 11 (2014). https://doi.org/10.1007/JHEP11(2014)011
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DOI: https://doi.org/10.1007/JHEP11(2014)011