Abstract
By fast Lyapunov indicator (FLI), we study the chaotic dynamics of closed string around charged black brane with hyperscaling violation (HV). The Hawking temperature, Lifshitz dynamical exponent and HV exponent together affect the chaotic dynamics of this system. The temperature plays the role of driving the closed string to escape to infinity. There is a threshold value z∗ = 2, below which the string is captured by the black brane no matter where the string is placed at the beginning. However, when z > 2, the string escapes to infinity if it is placed near the black brane at the beginning, but if the initial position of string is far away from the black brane, it oscillates around the black brane till eternity, which is a quasi-periodic motion. HV exponent plays the role of driving the string falling into the black brane. With the increase of HV exponent θ, the falling velocity becomes faster. We find that when we heat the system with large HV exponent, the chaotic system does not essentially changes. It indicates that the HV exponent plays a very important role in determining the state of the chaotic system. Also we study the effect from the winding number of the string. The study indicates that the chaotic dynamics of the string is insensitive to the winding number.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
B. Carter, Global structure of the Kerr family of gravitational fields, Phys. Rev.174 (1968) 1559.
S.D. Majumdar, A Class of Exact Solutions of Einstein’s Field Equations, Phys. Rev.72 (1947) 390.
C.P. Dettmann, N.E. Frankel and N.J. Cornish, Fractal basins and chaotic trajectories in multi-black hole space-times, Phys. Rev.D 50 (1994) R618 [gr-qc/9402027] [INSPIRE].
W. Hanan and E. Radu, Chaotic motion in multi-black hole spacetimes and holographic screens, Mod. Phys. Lett.A 22 (2007) 399 [gr-qc/0610119] [INSPIRE].
H. Varvoglis and D. Papadopoulos, Chaotic interaction of charged particles with a gravitational wave, Astron. Astrophys.261 (1992) 664.
V. Karas and D. Vokrouhlicky, Chaotic motion of test particles in the Ernst space-time, Gen. Rel. Grav.24 (1992) 729.
L. Bombelli and E. Calzetta, Chaos around a black hole, Class. Quant. Grav.9 (1992) 2573 [INSPIRE].
J.M. Aguirregabiria, Chaotic scattering around black holes, Phys. Lett.A 224 (1997) 234 [gr-qc/9604032] [INSPIRE].
Y. Sota, S. Suzuki and K.-i. Maeda, Chaos in static axisymmetric space-times. 1: Vacuum case, Class. Quant. Grav.13 (1996) 1241 [gr-qc/9505036] [INSPIRE].
S. Chen, M. Wang and J. Jing, Chaotic motion of particles in the accelerating and rotating black holes spacetime, JHEP09 (2016) 082 [arXiv:1604.02785] [INSPIRE].
A.V. Frolov and A.L. Larsen, Chaotic scattering and capture of strings by black hole, Class. Quant. Grav.16 (1999) 3717 [gr-qc/9908039] [INSPIRE].
D. Giataganas and K. Sfetsos, Non-integrability in non-relativistic theories, JHEP06 (2014) 018 [arXiv:1403.2703] [INSPIRE].
D. Giataganas, L.A. Pando Zayas and K. Zoubos, On Marginal Deformations and Non-Integrability, JHEP01 (2014) 129 [arXiv:1311.3241] [INSPIRE].
D. Giataganas and K. Zoubos, Non-integrability and Chaos with Unquenched Flavor, JHEP10 (2017) 042 [arXiv:1707.04033] [INSPIRE].
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].
S.S. Gubser, I.R. Klebanov and A.M. Polyakov, Gauge theory correlators from noncritical string theory, Phys. Lett.B 428 (1998) 105 [hep-th/9802109] [INSPIRE].
E. Witten, Anti-de Sitter space and holography, Adv. Theor. Math. Phys.2 (1998) 253 [hep-th/9802150] [INSPIRE].
O. Aharony, S.S. Gubser, J.M. Maldacena, H. Ooguri and Y. Oz, Large N field theories, string theory and gravity, Phys. Rept.323 (2000) 183 [hep-th/9905111] [INSPIRE].
L.A. Pando Zayas and C.A. Terrero-Escalante, Chaos in the Gauge / Gravity Correspondence, JHEP09 (2010) 094 [arXiv:1007.0277] [INSPIRE].
S.S. Gubser, I.R. Klebanov and A.M. Polyakov, A semiclassical limit of the gauge/string correspondence, Nucl. Phys.B 636 (2002) 99 [hep-th/0204051] [INSPIRE].
D.-Z. Ma, J.-P. Wu and J. Zhang, Chaos from the ring string in a Gauss-Bonnet black hole in AdS5 space, Phys. Rev.D 89 (2014) 086011 [arXiv:1405.3563] [INSPIRE].
X. Bai, B.-H. Lee, T. Moon and J. Chen, Chaos in Lifshitz Spacetimes, J. Korean Phys. Soc.68 (2016) 639 [arXiv:1406.5816] [INSPIRE].
P. Basu, P. Chaturvedi and P. Samantray, Chaotic dynamics of strings in charged black hole backgrounds, Phys. Rev.D 95 (2017) 066014 [arXiv:1607.04466] [INSPIRE].
T. Ishii, K. Murata and K. Yoshida, Fate of chaotic strings in a confining geometry, Phys. Rev.D 95 (2017) 066019 [arXiv:1610.05833] [INSPIRE].
M. Čubrovíc, The bound on chaos for closed strings in Anti-de Sitter black hole backgrounds, JHEP12 (2019) 150 [arXiv:1904.06295] [INSPIRE].
D.S. Fisher, Scaling and critical slowing down in random-field Ising systems, Phys. Rev. Lett.56 (1986) 416 [INSPIRE].
B. Gouteraux and E. Kiritsis, Generalized Holographic Quantum Criticality at Finite Density, JHEP12 (2011) 036 [arXiv:1107.2116] [INSPIRE].
L. Huijse, S. Sachdev and B. Swingle, Hidden Fermi surfaces in compressible states of gauge-gravity duality, Phys. Rev.B 85 (2012) 035121 [arXiv:1112.0573] [INSPIRE].
X. Dong, S. Harrison, S. Kachru, G. Torroba and H. Wang, Aspects of holography for theories with hyperscaling violation, JHEP06 (2012) 041 [arXiv:1201.1905] [INSPIRE].
C. Charmousis, B. Gouteraux, B.S. Kim, E. Kiritsis and R. Meyer, Effective Holographic Theories for low-temperature condensed matter systems, JHEP11 (2010) 151 [arXiv:1005.4690] [INSPIRE].
M.M. Wolf, Violation of the entropic area law for Fermions, Phys. Rev. Lett.96 (2006) 010404 [quant-ph/0503219] [INSPIRE].
B. Swingle, Entanglement Entropy and the Fermi Surface, Phys. Rev. Lett.105 (2010) 050502 [arXiv:0908.1724] [INSPIRE].
X.-M. Kuang, E. Papantonopoulos, B. Wang and J.-P. Wu, Formation of Fermi surfaces and the appearance of liquid phases in holographic theories with hyperscaling violation, JHEP11 (2014) 086 [arXiv:1409.2945] [INSPIRE].
X.-M. Kuang, E. Papantonopoulos, B. Wang and J.-P. Wu, Dynamically generated gap from holography in the charged black brane with hyperscaling violation, JHEP04 (2015) 137 [arXiv:1411.5627] [INSPIRE].
M. Alishahiha, E. O Colgain and H. Yavartanoo, Charged Black Branes with Hyperscaling Violating Factor, JHEP11 (2012) 137 [arXiv:1209.3946] [INSPIRE].
P. Basu and L.A. Pando Zayas, Analytic Non-integrability in String Theory, Phys. Rev.D 84 (2011) 046006 [arXiv:1105.2540] [INSPIRE].
P. Basu and L.A. Pando Zayas, Chaos rules out integrability of strings on AdS5× T1,1, Phys. Lett.B 700 (2011) 243 [arXiv:1103.4107] [INSPIRE].
P. Basu, D. Das and A. Ghosh, Integrability Lost, Phys. Lett.B 699 (2011) 388 [arXiv:1103.4101] [INSPIRE].
D.Z. Ma, X. Wu and J.F. Zhu, Velocity scaling method to correct individual Kepler energies, New Astron.13 (2008) 216.
D.Z. Ma, X. Wu and F.Y. Liu, Velocity corrections to Kepler energy and Laplace integral, Int. J. Mod. Phys.C 19 (2008) 1411.
D.Z. Ma, X. Wu and S.Y. Zhong, Eetending Nacozy’s approach to correct all orbital elements for each of multiple bodies, Astrophys. J.687 (2008) 1294.
J.R. Buchler and G. Kovacs, Period doubling bifurcations and chaos in W Virginis models, Astron. J.320 (1987) 57.
A.J. Maciejewski and S.M. Rybicki, Global bifurcations of periodic solutions of the Hill lunar problem, Celest. Mech. Dyn. Astron.81 (2001) 279.
J. Levin, Gravity waves, chaos, and spinning compact binaries, Phys. Rev. Lett.84 (2000) 3515.
Y.G. Markov, Application of Poincare periodic solutions to the study of the moon’s rotational motion, Sov. Astron.24 (1980) 228.
J.P. Eckmann and D. Ruelle, Ergodic theory of chaos and strange attractors, Rev. Mod. Phys.57 (1985) 617 [INSPIRE].
E. Ott, Chaos in Dynamical Systems, Cambridge University Press, (1993).
C. Skokos, The Lyapunov Characteristic Exponents and their computation, Lect. Notes Phys.790 (2010) 63 [arXiv:0811.0882] [INSPIRE].
G. Huang and X. Wu, Dynamics of the post-Newtonian circular restricted three-body problem with compact objects, Phys. Rev.D 89 (2014) 124034 [INSPIRE].
X. Wu and T.-y. Huang, Computation of Lyapunov exponents in general relativity, Phys. Lett.A 313 (2003) 77 [gr-qc/0302118] [INSPIRE].
C. Froeschlé, E. Lega and R. Gonczi, Fast Lyapunov indicators. Application to asteroidal motion, Celest. Mech. Dyn. Astron.67 (1997) 41.
C. Froeschlé and E. Lega, On the structure of symplectic mappings. The fast Lyapunov indicator: A very sensitive tool, Celest. Mech. Dyn. Astron.78 (2000) 167.
Z. Sándor, B. Érdi and Ch. Éfthymiopoulos, The phase space structure around L4 in the restricted three-body problem, Celest. Mech. Dyn. Astron.78 (2000) 11.
Z. Sándor, B. Érdi, A. Sźell and B. Funk, The relative Lyapunov indicator: an efficient method of chaos detection, Celest. Mech. Dyn. Astron.90 (2004) 127.
C. Skokos, Alignment indices: a new, simple method for determining the ordered or chaotic nature of orbits, J. Phys.A 34 (2001) 10029.
C. Skokos, C. Antonopoulos, T.C. Bountis and M.N. Vrahatis, Detecting order and chaos in Hamiltonian systems by the SALI method, J. Phys.A 37 (2004) 6269 [nlin/0404058] [INSPIRE].
P. Soulis, T. Bountis and R. Dvorak, Stability of motion in the Sitnikov 3-body problem, Celest. Mech. Dyn. Astron.99 (2007) 129.
P.S. Soulis, K.E. Papadakis and T. Bountis, Periodic orbits and bifurcations in the Sitnikov four-body problem, Celest. Mech. Dyn. Astron.100 (2008) 251.
T. Bountis and K.E. Papadakis, The stability of vertical motion in the N-body circular Sitnikov problem, Celest. Mech. Dyn. Astron.104 (2009) 205.
C. Skokos, T.C. Bountis and C. Antonopoulos, Geometrical properties of local dynamics in Hamiltonian systems: the generalized alignment index (GALI) method, PhysicaD 231 (2007) 30.
C. Skokos and T. Manos, The Smaller (SALI) and the Generalized (GALI) Alignment Indices: Efficient Methods of Chaos Detection, Lect. Notes Phys.915 (2016) 129 [arXiv:1412.7401] [INSPIRE].
X. Wu and G. Huang, Ruling out chaos in comparable mass compact binary systems with one body spinning, Mon. Not. Roy. Astron. Soc.452 (2015) 3167 [INSPIRE].
D.Z. Ma, Z, C. Long and Y. Zhu, Application of indicators for chaos in chaotic circuit systems, Int. J. Bifurcat. Chaos26 (2016) 1650182.
L. Susskind, Why do Things Fall?, arXiv:1802.01198 [INSPIRE].
T. Andrade and B. Withers, A simple holographic model of momentum relaxation, JHEP05 (2014) 101 [arXiv:1311.5157] [INSPIRE].
A. Donos and J.P. Gauntlett, Holographic Q-lattices, JHEP04 (2014) 040 [arXiv:1311.3292] [INSPIRE].
D. Vegh, Holography without translational symmetry, arXiv:1301.0537 [INSPIRE].
M. Wang, S. Chen and J. Jing, Chaos in the motion of a test scalar particle coupling to the Einstein tensor in Schwarzschild-Melvin black hole spacetime, Eur. Phys. J.C 77 (2017) 208 [arXiv:1605.09506] [INSPIRE].
J. Maldacena, S.H. Shenker and D. Stanford, A bound on chaos, JHEP08 (2016) 106 [arXiv:1503.01409] [INSPIRE].
K. Hashimoto and N. Tanahashi, Universality in Chaos of Particle Motion near Black Hole Horizon, Phys. Rev.D 95 (2017) 024007 [arXiv:1610.06070] [INSPIRE].
S. Dalui, B.R. Majhi and P. Mishra, Presence of horizon makes particle motion chaotic, Phys. Lett.B 788 (2019) 486 [arXiv:1803.06527] [INSPIRE].
S. Dalui, B.R. Majhi and P. Mishra, Horizon induces instability and creates quantum thermality, arXiv:1910.07989 [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: 1911.09913
Rights and permissions
This article is published under an open access license. Please check the 'Copyright Information' section either on this page or in the PDF for details of this license and what re-use is permitted. If your intended use exceeds what is permitted by the license or if you are unable to locate the licence and re-use information, please contact the Rights and Permissions team.
About this article
Cite this article
Ma, DZ., Zhang, D., Fu, G. et al. Chaotic dynamics of string around charged black brane with hyperscaling violation. J. High Energ. Phys. 2020, 103 (2020). https://doi.org/10.1007/JHEP01(2020)103
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP01(2020)103