Abstract
We reconsider the issue of whether scalar-tensor theories can admit stable wormhole configurations supported by a non-trivial radial profile for the scalar field. Using a recently proposed effective theory for perturbations around static, spherically symmetric backgrounds, we show that scalar-tensor theories of “beyond Horndeski” type can have wormhole solutions that are free of ghost and gradient instabilities. Such solutions are instead forbidden within the more restrictive “Horndeski” class of theories.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
A. Einstein and N. Rosen, The particle problem in the general theory of relativity, Phys. Rev. 48 (1935) 73 [INSPIRE].
M.S. Morris and K.S. Thorne, Wormholes in spacetime and their use for interstellar travel: a tool for teaching general relativity, Amer. J. Phys. 56 (1988) 395.
M. Visser, Lorentzian wormholes: from Einstein to Hawking, American Institute of Physics, Woodbury, NY, U.S.A. (1995) [INSPIRE].
P. Gao, D.L. Jafferis and A. Wall, Traversable wormholes via a double trace deformation, JHEP 12 (2017) 151 [arXiv:1608.05687] [INSPIRE].
J. Maldacena and X.-L. Qi, Eternal traversable wormhole, arXiv:1804.00491 [INSPIRE].
E. Caceres, A.S. Misobuchi and M.-L. Xiao, Rotating traversable wormholes in AdS, JHEP 12 (2018) 005 [arXiv:1807.07239] [INSPIRE].
Z. Fu, B. Grado-White and D. Marolf, A perturbative perspective on self-supporting wormholes, arXiv:1807.07917 [INSPIRE].
J. Maldacena, A. Milekhin and F. Popov, Traversable wormholes in four dimensions, arXiv:1807.04726 [INSPIRE].
S. Dubovsky, T. Gregoire, A. Nicolis and R. Rattazzi, Null energy condition and superluminal propagation, JHEP 03 (2006) 025 [hep-th/0512260] [INSPIRE].
V.A. Rubakov, The null energy condition and its violation, Phys. Usp. 57 (2014) 128 [Usp. Fiz. Nauk 184 (2014) 137] [arXiv:1401.4024] [INSPIRE].
C. Armendariz-Picon, On a class of stable, traversable Lorentzian wormholes in classical general relativity, Phys. Rev. D 65 (2002) 104010 [gr-qc/0201027] [INSPIRE].
K.A. Bronnikov and S. Grinyok, Instability of wormholes with a nonminimally coupled scalar field, Grav. Cosmol. 7 (2001) 297 [gr-qc/0201083] [INSPIRE].
K.A. Bronnikov and S. Grinyok, Charged wormholes with nonminimally coupled scalar fields, existence and stability, gr-qc/0205131 [INSPIRE].
K.A. Bronnikov and A.A. Starobinsky, No realistic wormholes from ghost-free scalar-tensor phantom dark energy, JETP Lett. 85 (2007) 1 [Pisma Zh. Eksp. Teor. Fiz. 85 (2007) 3] [gr-qc/0612032] [INSPIRE].
J.A. Gonzalez, F.S. Guzman and O. Sarbach, Instability of wormholes supported by a ghost scalar field. I. Linear stability analysis, Class. Quant. Grav. 26 (2009) 015010 [arXiv:0806.0608] [INSPIRE].
J.A. Gonzalez, F.S. Guzman and O. Sarbach, Instability of wormholes supported by a ghost scalar field. II. Nonlinear evolution, Class. Quant. Grav. 26 (2009) 015011 [arXiv:0806.1370] [INSPIRE].
V.A. Rubakov, Can Galileons support Lorentzian wormholes?, Theor. Math. Phys. 187 (2016) 743 [Teor. Mat. Fiz. 187 (2016) 338] [arXiv:1509.08808] [INSPIRE].
V.A. Rubakov, More about wormholes in generalized Galileon theories, Theor. Math. Phys. 188 (2016) 1253 [Teor. Mat. Fiz. 188 (2016) 337] [arXiv:1601.06566] [INSPIRE].
O.A. Evseev and O.I. Melichev, No static spherically symmetric wormholes in Horndeski theory, Phys. Rev. D 97 (2018) 124040 [arXiv:1711.04152] [INSPIRE].
P. Creminelli, D. Pirtskhalava, L. Santoni and E. Trincherini, Stability of geodesically complete cosmologies, JCAP 11 (2016) 047 [arXiv:1610.04207] [INSPIRE].
Y. Cai, Y. Wan, H.-G. Li, T. Qiu and Y.-S. Piao, The effective field theory of nonsingular cosmology, JHEP 01 (2017) 090 [arXiv:1610.03400] [INSPIRE].
G. Franciolini, L. Hui, R. Penco, L. Santoni and E. Trincherini, Effective field theory of black hole quasinormal modes in scalar-tensor theories, arXiv:1810.07706 [INSPIRE].
M. Libanov, S. Mironov and V. Rubakov, Generalized Galileons: instabilities of bouncing and genesis cosmologies and modified genesis, JCAP 08 (2016) 037 [arXiv:1605.05992] [INSPIRE].
T. Kobayashi, Generic instabilities of nonsingular cosmologies in Horndeski theory: a no-go theorem, Phys. Rev. D 94 (2016) 043511 [arXiv:1606.05831] [INSPIRE].
S. Mironov, V. Rubakov and V. Volkova, Towards wormhole beyond Horndeski, EPJ Web Conf. 191 (2018) 07014 [arXiv:1811.05832] [INSPIRE].
S. Mironov, V. Rubakov and V. Volkova, More about stable wormholes in beyond Horndeski theory, arXiv:1812.07022 [INSPIRE].
J. Gleyzes, D. Langlois, F. Piazza and F. Vernizzi, Healthy theories beyond Horndeski, Phys. Rev. Lett. 114 (2015) 211101 [arXiv:1404.6495] [INSPIRE].
M. Zumalacárregui and J. García-Bellido, Transforming gravity: from derivative couplings to matter to second-order scalar-tensor theories beyond the Horndeski Lagrangian, Phys. Rev. D 89 (2014) 064046 [arXiv:1308.4685] [INSPIRE].
D. Pirtskhalava, L. Santoni, E. Trincherini and F. Vernizzi, Weakly broken Galileon symmetry, JCAP 09 (2015) 007 [arXiv:1505.00007] [INSPIRE].
L. Santoni, E. Trincherini and L.G. Trombetta, Behind Horndeski: structurally robust higher derivative EFTs, JHEP 08 (2018) 118 [arXiv:1806.10073] [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].
G.W. Horndeski, Second-order scalar-tensor field equations in a four-dimensional space, Int. J. Theor. Phys. 10 (1974) 363 [INSPIRE].
C. Deffayet, X. Gao, D.A. Steer and G. Zahariade, From k-essence to generalised Galileons, Phys. Rev. D 84 (2011) 064039 [arXiv:1103.3260] [INSPIRE].
T. Regge and J.A. Wheeler, Stability of a Schwarzschild singularity, Phys. Rev. 108 (1957) 1063 [INSPIRE].
T. Kobayashi, H. Motohashi and T. Suyama, Black hole perturbation in the most general scalar-tensor theory with second-order field equations I: the odd-parity sector, Phys. Rev. D 85 (2012) 084025 [Erratum ibid. D 96 (2017) 109903] [arXiv:1202.4893] [INSPIRE].
T. Kobayashi, H. Motohashi and T. Suyama, Black hole perturbation in the most general scalar-tensor theory with second-order field equations II: the even-parity sector, Phys. Rev. D 89 (2014) 084042 [arXiv:1402.6740] [INSPIRE].
J.D. Bekenstein, The relation between physical and gravitational geometry, Phys. Rev. D 48 (1993) 3641 [gr-qc/9211017] [INSPIRE].
J. Gleyzes, D. Langlois and F. Vernizzi, A unifying description of dark energy, Int. J. Mod. Phys. D 23 (2015) 1443010 [arXiv:1411.3712] [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: 1811.05481
Rights and permissions
Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, 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 licence, and indicate if changes were made.
The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder.
To view a copy of this licence, visit https://creativecommons.org/licenses/by/4.0/.
About this article
Cite this article
Franciolini, G., Hui, L., Penco, R. et al. Stable wormholes in scalar-tensor theories. J. High Energ. Phys. 2019, 221 (2019). https://doi.org/10.1007/JHEP01(2019)221
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP01(2019)221