Abstract
We present a class of exact scalar-tensor black holes for a shift-symmetric part of the Horndeski action. The action includes a higher order scalar tensor interaction term. We find that for a static and spherically symmetric space-time, the scalar field, if time dependent, can be non-trivial and regular thus circumventing in an interesting way no-hair arguments for gallileons. Furthermore, within this class we find a stealth Schwarzschild and a partially self-tuned de-Sitter Schwarzschild black hole, both exhibiting a non trivial and regular space and time dependent scalar. In the latter solution the bulk vacuum energy is screened from a necessarily smaller geometric effective de Sitter vacuum via an integration constant associated to the time dependent scalar field.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
C. Charmousis, E.J. Copeland, A. Padilla and P.M. Saffin, Self-tuning and the derivation of a class of scalar-tensor theories, Phys. Rev. D 85 (2012) 104040 [arXiv:1112.4866] [INSPIRE].
C. Charmousis, E.J. Copeland, A. Padilla and P.M. Saffin, General second order scalar-tensor theory, self tuning and the fab four, Phys. Rev. Lett. 108 (2012) 051101 [arXiv:1106.2000] [INSPIRE].
G.W. Horndeski, Second-order scalar-tensor field equations in a four-dimensional space, Int. J. Theor. Phys. 10 (1974) 363 [INSPIRE].
A. Nicolis, R. Rattazzi and E. Trincherini, The Galileon as a local modification of gravity, Phys. Rev. D 79 (2009) 064036 [arXiv:0811.2197] [INSPIRE].
C. Deffayet, G. Esposito-Farese and A. Vikman, Covariant Galileon, Phys. Rev. D 79 (2009) 084003 [arXiv:0901.1314] [INSPIRE].
C. Deffayet, S. Deser and G. Esposito-Farese, Generalized Galileons: all scalar models whose curved background extensions maintain second-order field equations and stress-tensors, Phys. Rev. D 80 (2009) 064015 [arXiv:0906.1967] [INSPIRE].
C. Charmousis, B. Gouteraux and E. Kiritsis, Higher-derivative scalar-vector-tensor theories: black holes, Galileons, singularity cloaking and holography, JHEP 09 (2012) 011 [arXiv:1206.1499] [INSPIRE].
M. Rinaldi, Black holes with non-minimal derivative coupling, Phys. Rev. D 86 (2012) 084048 [arXiv:1208.0103] [INSPIRE].
J.D. Bekenstein, Black holes: classical properties, thermodynamics and heuristic quantization, gr-qc/9808028 [INSPIRE].
G. Gubitosi and E.V. Linder, Purely kinetic coupled gravity, Phys. Lett. B 703 (2011) 113 [arXiv:1106.2815] [INSPIRE].
L. Hui and A. Nicolis, No-hair theorem for the Galileon, Phys. Rev. Lett. 110 (2013) 241104 [arXiv:1202.1296] [INSPIRE].
C. Germani, L. Martucci and P. Moyassari, Introducing the Slotheon: a slow Galileon scalar field in curved space-time, Phys. Rev. D 85 (2012) 103501 [arXiv:1108.1406] [INSPIRE].
N.M. Bocharova, K.A. Bronnikov and V.N. Melnikov, An exact solution of the system of einstein equations and mass-free scalar field, Vestn. Mosk. Univ. Fiz. Astro. 6 (1970) 706.
J.D. Bekenstein, Exact solutions of Einstein conformal scalar equations, Annals Phys. 82 (1974) 535 [INSPIRE].
E. Babichev, Galileon accretion, Phys. Rev. D 83 (2011) 024008 [arXiv:1009.2921] [INSPIRE].
E. Babichev, C. Deffayet and G. Esposito-Farese, Constraints on shift-symmetric scalar-tensor theories with a Vainshtein mechanism from bounds on the time variation of G, Phys. Rev. Lett. 107 (2011) 251102 [arXiv:1107.1569] [INSPIRE].
E. Babichev and G. Esposito-Farese, Time-dependent spherically symmetric covariant Galileons, Phys. Rev. D 87 (2013) 044032 [arXiv:1212.1394] [INSPIRE].
L.I. Petrich, S.L. Shapiro and S.A. Teukolsky, Accretion onto a moving black hole: an exact solution, Phys. Rev. Lett. 60 (1988) 1781 [INSPIRE].
T. Jacobson, Primordial black hole evolution in tensor scalar cosmology, Phys. Rev. Lett. 83 (1999) 2699 [astro-ph/9905303] [INSPIRE].
E. Ayon-Beato, C. Martinez and J. Zanelli, Stealth scalar field overflying a (2 + 1) black hole, Gen. Rel. Grav. 38 (2006) 145 [hep-th/0403228] [INSPIRE].
C. Deffayet, O. Pujolàs, I. Sawicki and A. Vikman, Imperfect dark energy from kinetic gravity braiding, JCAP 10 (2010) 026 [arXiv:1008.0048] [INSPIRE].
M.J. Bowick, S.B. Giddings, J.A. Harvey, G.T. Horowitz and A. Strominger, Axionic black holes and a Bohm-Aharonov effect for strings, Phys. Rev. Lett. 61 (1988) 2823 [INSPIRE].
Y. Bardoux, M.M. Caldarelli and C. Charmousis, Shaping black holes with free fields, JHEP 05 (2012) 054 [arXiv:1202.4458] [INSPIRE].
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.
Author information
Authors and Affiliations
Corresponding author
Additional information
ArXiv ePrint: 1312.3204
Rights and permissions
Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (https://creativecommons.org/licenses/by/4.0), which permits use, duplication, adaptation, distribution, and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
About this article
Cite this article
Babichev, E., Charmousis, C. Dressing a black hole with a time-dependent Galileon. J. High Energ. Phys. 2014, 106 (2014). https://doi.org/10.1007/JHEP08(2014)106
Received:
Revised:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP08(2014)106