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Holographic entanglement entropy for black strings

  • Yuanceng Xu
  • Mengjie Wang
  • Jiliang JingEmail author
Research Article
  • 39 Downloads

Abstract

The holographic entanglement entropy (HEE) of field theories dual to 4-dimensional black strings with both the infinity boundary and near the horizon is investigated. It is shown that, with the infinity boundary, the main contribution of the HEE is divergent and it comes from the AdS background. If we remove this contribution, the remaining part is finite and proportional to the mass and charge densities. Near the horizon, we find that the HEE equals the Bekenstein–Hawking entropy if the subsystem covers the whole conformal boundary, for both charged and uncharged cases. In particular, the minimal surface (Ryu–Takayanagi surface) always stays in the bulk region for uncharged and non-extremal charged cases, while it is immersed inside the boundary for extremal black string.

Keywords

Holographic entanglement entropy Bekenstein–Hawking entropy Black string 

Notes

Acknowledgements

This work is supported by the National Natural Science Foundation of China under Grant Nos. 11875025.

References

  1. 1.
    ’t Hooft, G.: On the quantum structure of a black hole. Nucl. Phys. B 256, 727 (1985)ADSMathSciNetCrossRefGoogle Scholar
  2. 2.
    Mann, R.B., Tarasov, L., Zelnikov, A.: Brick walls for black holes. Class. Quantum Grav. 9, 1487 (1992)ADSMathSciNetCrossRefGoogle Scholar
  3. 3.
    Wald, R.M.: Black hole entropy is the Noether charge. Phys. Rev. D 48, R3427(R) (1993)ADSMathSciNetCrossRefGoogle Scholar
  4. 4.
    Jing, J.: Asymptotic structure near event horizon and Cardy–Verlinde formula for general asymptotically flat stationary black hole. Phys. Lett. B 705, 287 (2011)ADSMathSciNetCrossRefGoogle Scholar
  5. 5.
    Jing, J.: Cardy–Verlinde Formula and entropy bounds in Kerr–Newman-AdS4 /dS4 black holes backgrounds. Phys. Rev. D 66, 024002 (2002)ADSMathSciNetCrossRefGoogle Scholar
  6. 6.
    Jing, J.: Quantum entropy of the Kerr black hole arising from the gravitational perturbation. Phys. Rev. D 64, 064015 (2001)ADSMathSciNetCrossRefGoogle Scholar
  7. 7.
    Jing, J.: Effect of spins on quantum entropy of black holes. Phys. Rev. D 63, 084028 (2001)ADSMathSciNetCrossRefGoogle Scholar
  8. 8.
    Jing, J., Yan, M.: Statistical entropy of a stationary dilaton black holes from Cardy formula. Phys. Rev. D 63, 024003 (2001)ADSMathSciNetCrossRefGoogle Scholar
  9. 9.
    Jing, J., Yan, M.: Entropies of rotating charged black holes from conformal field theory at Killing horizons. Phys. Rev. D 62, 104013 (2000)ADSMathSciNetCrossRefGoogle Scholar
  10. 10.
    Jing, J., Yan, M.: Entropies of the general stationary non-extreme axisymmetric black hole: statistical-mechanical and thermodynamics. Phys. Rev. D 61, 044016 (2000)ADSMathSciNetCrossRefGoogle Scholar
  11. 11.
    Jing, J., Yan, M.: Quantum entropy of a nonextreme stationary axisymmetric black hole due to a minimally coupled quantum scalar field. Phys. Rev. D 60, 084015 (1999)ADSMathSciNetCrossRefGoogle Scholar
  12. 12.
    Bekenstein, J.D.: Black holes and entropy. Phys. Rev. D 7, 2333 (1973)ADSMathSciNetCrossRefGoogle Scholar
  13. 13.
    Bombelli, L., Koul, R.K., Lee, J., Sorkin, R.D.: Quantum source of entropy for black holes. Phys. Rev. D 34, 373 (1986)ADSMathSciNetCrossRefGoogle Scholar
  14. 14.
    Nielsen, M.A., Chuang, I.L.: Quantum compution and quantum communication. Cambridge University Press, Cambridge (2000)Google Scholar
  15. 15.
    Solodukhin, S.N.: Entanglement entropy of black holes. Living Rev. Relativ. 14, 8 (2011)ADSCrossRefGoogle Scholar
  16. 16.
    Strominger, A., Vafa, C.: Microscopic origin of the Bekenstein–Hawking entropy. Phys. Lett. B. 379, 99 (1996)ADSMathSciNetCrossRefGoogle Scholar
  17. 17.
    ’t Hooft, G.: Dimensional reduction in quantum gravity, Salamfest 1993:0284-296, THU-93/26Google Scholar
  18. 18.
    Susskind, L.: The world as a hologram. J. Math. Phys. 36, 6377 (1995)ADSMathSciNetCrossRefGoogle Scholar
  19. 19.
    Maldacena, J.M.: The large N limit of superconformal field theories and supergravity. Adv. Theor. Math. Phys. 2, 231 (1998)ADSMathSciNetCrossRefGoogle Scholar
  20. 20.
    Ryu, S., Takayanagi, T.: Holographic derivation of entanglement entropy from \(AdS/CFT\). Phys. Rev. Lett. 96, 181602 (2006)ADSMathSciNetCrossRefGoogle Scholar
  21. 21.
    Ryu, S., Takayanagi, T.: Aspects of holographic entanglement entropy. JHEP 0608, 045 (2006)ADSMathSciNetCrossRefGoogle Scholar
  22. 22.
    Bah, L., Faraggi, A.: Holographic entanglement entropy at finite temperature. Int. J. Mod. Phys. A 24, 2703–2728 (2009)ADSMathSciNetCrossRefGoogle Scholar
  23. 23.
    Cadoni, M., Melis, M.: Holographic entanglement entropy of BTZ black hole. Found. Phys. 40, 638–657 (2010)ADSMathSciNetCrossRefGoogle Scholar
  24. 24.
    Abajo-Arrastia, J., Aparicio, J.: Holographic evolution of entanglement entropy. JHEP 1011, 149 (2010)ADSCrossRefGoogle Scholar
  25. 25.
    Albash, T., Johnson, C.V.: Evolution of holographic entanglement entropy after thermal and electromagnetic quenches. New J. Phys. 13, 045017 (2011)ADSCrossRefGoogle Scholar
  26. 26.
    Ecker, C., Grumiller, D., Stricker, S.A.: Evolution of holographic entanglement entropy in an anisotropic system. JHEP 1507, 146 (2015)ADSMathSciNetCrossRefGoogle Scholar
  27. 27.
    kim, N., Lee, J.H.: Time-evolution of the holographic entanglement entropy and metric perturbations. J. Korean Phys. Soc. 69(4), 623 (2016)ADSCrossRefGoogle Scholar
  28. 28.
    Kundu, S., Pedraza, J.F.: Spread of entanglement for small subsystems in holographic CFTs. Phys. Rev. D. 95, 086008 (2017)ADSMathSciNetCrossRefGoogle Scholar
  29. 29.
    Myers, R.C., Singh, A.: Comments on holographic entanglement entropy and RG flows. JHEP 1204, 122 (2012)ADSMathSciNetCrossRefGoogle Scholar
  30. 30.
    Caceres, E., Nguyen, P.H., Pedraza, J.F.: Holographic entanglement entropy and the extended phase structure of STU black holes. JHEP 1509, 184 (2015)ADSMathSciNetCrossRefGoogle Scholar
  31. 31.
    Johson, C.V.: Large \(N\) phase transitions, finite volume, and entanglement entropy. JHEP 1403, 047 (2014)ADSCrossRefGoogle Scholar
  32. 32.
    Nguyen, P.H.: An equal area law for holographic entanglement entropy of the AdS-RN black hole. JHEP 1512, 139 (2015)ADSMathSciNetzbMATHGoogle Scholar
  33. 33.
    Boer, J., Kulaxizi, M., Parnachev, A.: Holographic entanglement entropy in Lovelock gravities. JHEP 1107, 109 (2011)ADSMathSciNetCrossRefGoogle Scholar
  34. 34.
    Miao, R.X., Guo, W.Z.: Holographic entanglement entropy for the most general higher derivative gravity. JHEP 1508, 031 (2015)ADSMathSciNetCrossRefGoogle Scholar
  35. 35.
    Alishahiha, M., Astaneh, A.F., Mozaffar, M.R.M.: Holographic entanglement entropy for 4D conformal gravity. JHEP 1402, 008 (2014)ADSCrossRefGoogle Scholar
  36. 36.
    Zeng, X., Zhang, H., Li, L.: Phase transition of holographic entanglement entropy in massive gravity. Phys. Lett. B. 756, 170 (2016)ADSCrossRefGoogle Scholar
  37. 37.
    Pang, D.-W.: On holographic entanglement entropy of non-local field theories. Phys. Rev. D. 89, 126005 (2014)ADSCrossRefGoogle Scholar
  38. 38.
    Huang, S., Fang, X., Jing, J.: Numerical calculation of the entanglement entropy for scalar field in dilaton spacetimes. Gen. Relativ. Gravit. 50, 70 (2018)ADSMathSciNetCrossRefGoogle Scholar
  39. 39.
    Kim, K., Kwon, O.: Holographic entanglement entropy of mass-deformed ABJM theory. Phys. Rev. D. 90, 126003 (2014)ADSCrossRefGoogle Scholar
  40. 40.
    Fischler, W., Kundu, S., Pedraza, J.F.: Entanglement and out-of-equilibrium dynamics in holographic models of de Sitter QFTs. JHEP 1407, 021 (2014)ADSCrossRefGoogle Scholar
  41. 41.
    Fatima, A., Saifullah, K.: Thermodynamics of charged and rotating black strings. Astrophys. Space Sci. 341, 437 (2012)ADSCrossRefGoogle Scholar
  42. 42.
    Lemos, J.P.S., Zanchin, V.T.: Rotating charged black strings and three-dimensional black holes. Phys. Rev. D. 54, 3840 (1996)ADSMathSciNetCrossRefGoogle Scholar
  43. 43.
    Kundu, S., Pedraza, J.F.: Aspects of holographic entanglement at finite temperature and chemical potential. JHEP 1608, 177 (2016)ADSMathSciNetCrossRefGoogle Scholar
  44. 44.
    Sun, Y., Zhao, L.: Holographic entanglement entropies for Schwarzschild and Reisner–Nordström black holes in asymptotically Minkowski spacetimes. Phys. Rev. D. 95, 086014 (2017)ADSMathSciNetCrossRefGoogle Scholar
  45. 45.
    Cai, R.G., Zhang, Y.: Black plane solutions in four-dimensional spacetimes. Phys. Rev. D. 54, 4891 (1996)ADSMathSciNetCrossRefGoogle Scholar
  46. 46.
    Bhattacharya, J., Nozaki, M., Takayanagi, T., Ugajin, T.: Thermodynamical property of entanglement entropy for excited states. Phys. Rev. Lett. 110(9), 091602 (2013)ADSCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of Physics, Key Laboratory of Low Dimensional Quantum Structures and Quantum Control of Ministry of Education, and Synergetic Innovation Center for Quantum Effects and ApplicationsHunan Normal UniversityChangshaPeople’s Republic of China

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