Abstract
We investigate entanglement entropy in Gauss-Bonnet gravity following a global quench. It is known that in dynamical scenarios the entanglement entropy probe penetrates the apparent horizon. The goal of this work is to study how far behind the horizon can the entanglement probe reach in a Gauss-Bonnet theory. We find that the behavior is quite different depending on the sign of the Gauss-Bonnet coupling λGB. For λGB > 0 the behavior of the probes is just as in Einstein gravity; the probes do not reach the singularity but asymptote to a locus behind the apparent horizon. We calculate the minimum radial position rmin reached by the probes and show that for λGB > 0 they explore less of the spacetime behind the horizon than in Einstein gravity. On the other hand, for λGB < 0 the results are strikingly different; for early times a new family of solutions appears. These new solutions reach arbitrarily close to the singularity. We calculate the entanglement entropy for the two family of solutions with λGB < 0 and find that the ones that reach the singularity are the ones of less entanglement entropy. Thus, for λGB < 0 the holographic entanglement entropy probes further behind the horizon than in Einstein gravity. In fact, for early times it can explore all the way to the singularity.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
S. Ryu and T. Takayanagi, Holographic derivation of entanglement entropy from AdS/CFT, Phys. Rev. Lett. 96 (2006) 181602 [hep-th/0603001] [INSPIRE].
V.E. Hubeny, M. Rangamani and T. Takayanagi, A Covariant holographic entanglement entropy proposal, JHEP 07 (2007) 062 [arXiv:0705.0016] [INSPIRE].
J. Abajo-Arrastia, J. Aparicio and E. Lopez, Holographic Evolution of Entanglement Entropy, JHEP 11 (2010) 149 [arXiv:1006.4090] [INSPIRE].
V.E. Hubeny, H. Maxfield, M. Rangamani and E. Tonni, Holographic entanglement plateaux, JHEP 08 (2013) 092 [arXiv:1306.4004] [INSPIRE].
V.E. Hubeny and H. Maxfield, Holographic probes of collapsing black holes, JHEP 03 (2014) 097 [arXiv:1312.6887] [INSPIRE].
H. Liu and S.J. Suh, Entanglement growth during thermalization in holographic systems, Phys. Rev. D 89 (2014) 066012 [arXiv:1311.1200] [INSPIRE].
B. Freivogel, R.A. Jefferson, L. Kabir, B. Mosk and I.-S. Yang, Casting Shadows on Holographic Reconstruction, Phys. Rev. D 91 (2015) 086013 [arXiv:1412.5175] [INSPIRE].
V.E. Hubeny and M. Rangamani, Causal Holographic Information, JHEP 06 (2012) 114 [arXiv:1204.1698] [INSPIRE].
V. Balasubramanian, B.D. Chowdhury, B. Czech and J. de Boer, Entwinement and the emergence of spacetime, JHEP 01 (2015) 048 [arXiv:1406.5859] [INSPIRE].
Y.-Z. Li, S.-F. Wu and G.-H. Yang, Gauss-Bonnet correction to Holographic thermalization: two-point functions, circular Wilson loops and entanglement entropy, Phys. Rev. D 88 (2013) 086006 [arXiv:1309.3764] [INSPIRE].
X. Zeng and W. Liu, Holographic thermalization in Gauss-Bonnet gravity, Phys. Lett. B 726 (2013) 481 [arXiv:1305.4841] [INSPIRE].
X.-X. Zeng, X.-M. Liu and W.-B. Liu, Holographic thermalization with a chemical potential in Gauss-Bonnet gravity, JHEP 03 (2014) 031 [arXiv:1311.0718] [INSPIRE].
M. Brigante, H. Liu, R.C. Myers, S. Shenker and S. Yaida, Viscosity Bound Violation in Higher Derivative Gravity, Phys. Rev. D 77 (2008) 126006 [arXiv:0712.0805] [INSPIRE].
A. Buchel, R.C. Myers and A. Sinha, Beyond η/s = 1/4π, JHEP 03 (2009) 084 [arXiv:0812.2521] [INSPIRE].
J. de Boer, M. Kulaxizi and A. Parnachev, Holographic Lovelock Gravities and Black Holes, JHEP 06 (2010) 008 [arXiv:0912.1877] [INSPIRE].
A. Buchel, J. Escobedo, R.C. Myers, M.F. Paulos, A. Sinha and M. Smolkin, Holographic GB gravity in arbitrary dimensions, JHEP 03 (2010) 111 [arXiv:0911.4257] [INSPIRE].
Y. Kats and P. Petrov, Effect of curvature squared corrections in AdS on the viscosity of the dual gauge theory, JHEP 01 (2009) 044 [arXiv:0712.0743] [INSPIRE].
E. Shaverin and A. Yarom, Universality of second order transport in Gauss-Bonnet gravity, JHEP 04 (2013) 013 [arXiv:1211.1979] [INSPIRE].
V. Jahnke, A.S. Misobuchi and D. Trancanelli, Holographic renormalization and anisotropic black branes in higher curvature gravity, JHEP 01 (2015) 122 [arXiv:1411.5964] [INSPIRE].
X.O. Camanho, J.D. Edelstein, J. Maldacena and A. Zhiboedov, Causality Constraints on Corrections to the Graviton Three-Point Coupling, JHEP 02 (2016) 020 [arXiv:1407.5597] [INSPIRE].
S. Grozdanov, N. Kaplis and A.O. Starinets, From strong to weak coupling in holographic models of thermalization, JHEP 07 (2016) 151 [arXiv:1605.02173] [INSPIRE].
S. Grozdanov and A.O. Starinets, On the universal identity in second order hydrodynamics, JHEP 03 (2015) 007 [arXiv:1412.5685] [INSPIRE].
S. Grozdanov and A.O. Starinets, Second-order transport, quasinormal modes and zero-viscosity limit in the Gauss-Bonnet holographic fluid, JHEP 03 (2017) 166 [arXiv:1611.07053] [INSPIRE].
V. Balasubramanian et al., Holographic Thermalization, Phys. Rev. D 84 (2011) 026010 [arXiv:1103.2683] [INSPIRE].
E. Caceres and A. Kundu, Holographic Thermalization with Chemical Potential, JHEP 09 (2012) 055 [arXiv:1205.2354] [INSPIRE].
D. Galante and M. Schvellinger, Thermalization with a chemical potential from AdS spaces, JHEP 07 (2012) 096 [arXiv:1205.1548] [INSPIRE].
E. Caceres, A. Kundu and D.-L. Yang, Jet Quenching and Holographic Thermalization with a Chemical Potential, JHEP 03 (2014) 073 [arXiv:1212.5728] [INSPIRE].
L.-Y. Hung, R.C. Myers and M. Smolkin, On Holographic Entanglement Entropy and Higher Curvature Gravity, JHEP 04 (2011) 025 [arXiv:1101.5813] [INSPIRE].
J. de Boer, M. Kulaxizi and A. Parnachev, Holographic Entanglement Entropy in Lovelock Gravities, JHEP 07 (2011) 109 [arXiv:1101.5781] [INSPIRE].
X. Dong, Holographic Entanglement Entropy for General Higher Derivative Gravity, JHEP 01 (2014) 044 [arXiv:1310.5713] [INSPIRE].
J. Camps, Generalized entropy and higher derivative Gravity, JHEP 03 (2014) 070 [arXiv:1310.6659] [INSPIRE].
M. Headrick, V.E. Hubeny, A. Lawrence and M. Rangamani, Causality and holographic entanglement entropy, JHEP 12 (2014) 162 [arXiv:1408.6300] [INSPIRE].
J. Erdmenger, M. Flory and C. Sleight, Conditions on holographic entangling surfaces in higher curvature gravity, JHEP 06 (2014) 104 [arXiv:1401.5075] [INSPIRE].
X.O. Camanho and J.D. Edelstein, A Lovelock black hole bestiary, Class. Quant. Grav. 30 (2013) 035009 [arXiv:1103.3669] [INSPIRE].
R.C. Myers and A. Singh, Comments on Holographic Entanglement Entropy and RG Flows, JHEP 04 (2012) 122 [arXiv:1202.2068] [INSPIRE].
D.G. Boulware and S. Deser, String Generated Gravity Models, Phys. Rev. Lett. 55 (1985) 2656 [INSPIRE].
R.C. Myers and B. Robinson, Black Holes in Quasi-topological Gravity, JHEP 08 (2010) 067 [arXiv:1003.5357] [INSPIRE].
R.-G. Cai, Gauss-Bonnet black holes in AdS spaces, Phys. Rev. D 65 (2002) 084014 [hep-th/0109133] [INSPIRE].
R. Callan, J.-Y. He and M. Headrick, Strong subadditivity and the covariant holographic entanglement entropy formula, JHEP 06 (2012) 081 [arXiv:1204.2309] [INSPIRE].
E. Caceres, A. Kundu, J.F. Pedraza and W. Tangarife, Strong Subadditivity, Null Energy Condition and Charged Black Holes, JHEP 01 (2014) 084 [arXiv:1304.3398] [INSPIRE].
P. Figueras, V.E. Hubeny, M. Rangamani and S.F. Ross, Dynamical black holes and expanding plasmas, JHEP 04 (2009) 137 [arXiv:0902.4696] [INSPIRE].
J. Dormand and P. Prince, A family of embedded runge-kutta formulae, J. Comput. Appl. Math. 6 (1980) 19.
E. Hairer and G. Wanner, DoP853, (1994).
A. Allais and E. Tonni, Holographic evolution of the mutual information, JHEP 01 (2012) 102 [arXiv:1110.1607] [INSPIRE].
T. Andrade, E. Caceres and C. Keeler, Boundary Causality vs Hyperbolicity for Spherical Black Holes in Gauss-Bonnet, Class. Quant. Grav. 34 (2017) 135003 [arXiv:1610.06078] [INSPIRE].
P. Fonda, L. Franti, V. Keränen, E. Keski-Vakkuri, L. Thorlacius and E. Tonni, Holographic thermalization with Lifshitz scaling and hyperscaling violation, JHEP 08 (2014) 051 [arXiv:1401.6088] [INSPIRE].
M. Alishahiha, A. Faraji Astaneh and M.R. Mohammadi Mozaffar, Thermalization in backgrounds with hyperscaling violating factor, Phys. Rev. D 90 (2014) 046004 [arXiv:1401.2807] [INSPIRE].
P. Bueno and P.F. Ramirez, Higher-curvature corrections to holographic entanglement entropy in geometries with hyperscaling violation, JHEP 12 (2014) 078 [arXiv:1408.6380] [INSPIRE].
G. Knodel and J.T. Liu, Higher derivative corrections to Lifshitz backgrounds, JHEP 10 (2013) 002 [arXiv:1305.3279] [INSPIRE].
S. Bhattacharyya and S. Minwalla, Weak Field Black Hole Formation in Asymptotically AdS Spacetimes, JHEP 09 (2009) 034 [arXiv:0904.0464] [INSPIRE].
E. Caceres, A. Kundu, J.F. Pedraza and D.-L. Yang, Weak Field Collapse in AdS: Introducing a Charge Density, JHEP 06 (2015) 111 [arXiv:1411.1744] [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: 1512.05666
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
Caceres, E., Sanchez, M. & Virrueta, J. Holographic entanglement entropy in time dependent Gauss-Bonnet gravity. J. High Energ. Phys. 2017, 127 (2017). https://doi.org/10.1007/JHEP09(2017)127
Received:
Revised:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP09(2017)127