Skip to main content
SpringerLink
Log in

Anisotropic expansion, second-order hydrodynamics and holographic dual

  • Published:
Pramana Aims and scope Submit manuscript

Abstract

We consider Kasner space–time describing anisotropic three-dimensional expansion of RHIC and LHC fireball and study the generalisation of Bjorken’s one-dimensional expansion by taking into account second-order relativistic viscous hydrodynamics. Using time-dependent AdS/CFT correspondence, we study the late-time behaviour of the Bjorken flow. From the conditions of conformal invariance and energy–momentum conservation, we obtain the explicit expression for the energy density as a function of proper time in terms of Kasner parameters. The proper time dependence of the temperature and entropy have also been obtained in terms of Kasner parameters. We consider Eddington–Finkelstein-type coordinates and discuss the gravity dual of the anisotropically expanding fluid in the late-time regime.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. J M Maldacena, Adv. Theor. Math. Phys. 2, 231 (1998); Int. J. Theor. Phys. 38, 1113 (1999), arXiv:hep-th/9711200

  2. S S Gubser, I R Klebanov and A M Polyakov, Phys. Lett. B 428, 105 (1998), hep-th/9802109; E Witten, Adv. Theor. Math. Phys. 2, 253 (1998), arXiv:hep-th/9802150

    Article  ADS  MathSciNet  Google Scholar 

  3. E V Shuryak, Nucl. Phys. A 750, 64 (2005), arXiv:hep-ph/0405066

    Article  ADS  Google Scholar 

  4. P F Kolb and U Heinz, Hydrodynamic description of ultrarelativistic heavy-ion collisions, arXiv:nucl-th/0305084

  5. M J Tannenbaum, Rep. Prog. Phys. 69, 2005 (2006), arXiv:nucl-ex/0603003

    Article  ADS  Google Scholar 

  6. W Florkowski, M P Heller and M Spalinski, Rep. Prog. Phys. 81, 046001 (2018), arXiv:1707.02282 [hep-ph]

    Article  ADS  Google Scholar 

  7. G Policastro, D T Son and A O Starinets, Phys. Rev. Lett. 87, 081601, hep-th/0104066; G Policastro, D T Son and A O Starinets, JHEP 0209, 043 (2002), arXiv:hep-th/020505

  8. P Kovtun, D T Son and A O Starinets, Phys. Rev. Lett. 94, 111601 (2005), arXiv:hep-th/0405231

    Article  ADS  Google Scholar 

  9. I Müller, Z. Phys. 198, 329 (1967)

    Article  ADS  Google Scholar 

  10. W Israel and J M Stewart, Ann. Phys. 118, 341 (1979)

    Article  ADS  Google Scholar 

  11. J D Bjorken, Phys. Rev. D 27, 140 (1983)

    Article  ADS  Google Scholar 

  12. E Shuryak, S-J Sin and I Zahed, J. Korean Phys. Soc. 50, 384 (2007), arXiv:hep-th/0511199

    Article  Google Scholar 

  13. H Nastase, The RHIC fireball as a dual black hole, arXiv:hep-th/0501068

  14. R A Janik and R Peschanski, Phys. Rev. D 73, 045013 (2006), arXiv:hep-th/0512162

    Article  ADS  MathSciNet  Google Scholar 

  15. S de Haro, K Skenderis and S N Solodukhin, Commun. Math. Phys. 217, 595 (2001), arXiv:hep-th/0002230

    Article  ADS  Google Scholar 

  16. D Bak and R A Janik, Phys. Lett. B 645, 303 (2007), arXiv:hep-th/0611304

    Article  ADS  MathSciNet  Google Scholar 

  17. S Nakamura and S J Sin, JHEP 0609, 020 (2006), arXiv:hep-th/0607123

    Article  ADS  Google Scholar 

  18. S J Sin, S Nakamura and S P Kim, JHEP 0612, 075 (2006), arXiv:hep-th/0610113

    Article  ADS  Google Scholar 

  19. R Baier, P Romatschke, D T Son, A O Sterinets and M A Stephanov, JHEP 0804, 100 (2008), arXiv:0712.2451 [hep-th]

    Article  ADS  Google Scholar 

  20. S Bhattacharyya, V E Hubeny, S Minwalla and M Rangamani, JHEP 0802, 045 (2008), arXiv:0712.2456 [hep-th]

    Article  ADS  Google Scholar 

  21. M P Heller and R A Janik, Phys. Rev. D 76, 025027 (2007), arXiv:hep-th/0703.243

    Article  ADS  MathSciNet  Google Scholar 

  22. M P Heller, P Surowka, R Loganayagam, M Spalinski and S E Vazquez, Phys. Rev. Lett. 102, 041601 (2009), arXiv:0805.3774 [hep-th]

    Article  ADS  Google Scholar 

  23. S Kinoshita, S Mukohyama, S Nakamura and K Oda, Prog. Theor. Phys. 121, 121 (2009), arXiv:0807.3797 [hep-th]

    Article  ADS  Google Scholar 

  24. S Kinoshita, S Mukohyama, S Nakamura and K Oda, Phys. Rev. Lett. 102, 031601 (2009), arXiv:0901.4834 [hep-th]

    Article  ADS  MathSciNet  Google Scholar 

  25. P Figueras, V E Hubeny, M Rangamani and S F Ross, JHEP 0904, 137 (2009), arXiv:0902.4696 [hep-th]

    Article  ADS  Google Scholar 

  26. A Dash and A Jaiswal, Phys. Rev. D 97, 104005 (2018), arXiv:1711.07130 [gr-qc]

    Article  ADS  MathSciNet  Google Scholar 

  27. M Strickland, Acta Phys. Polon. 45(12), 2355 (2014), arXiv:1410.5786 [nucl-th]

  28. P Romatschke, Phys. Rev. Lett. 120, 012301 (2018), arXiv:1704.08699 [hep-th]

    Article  ADS  Google Scholar 

  29. M P Heller and M Splaniski, Phys. Rev. Lett. 115, 072501 (2015), arXiv:1503.07514 [hep-th]

    Article  ADS  Google Scholar 

  30. S Jaiswal, C Chattopadhyay, A Jaiswal, S Pal and U Heinz, Phys. Rev. C 100, 034901 (2019), arXiv:1907.07965 [nucl-th]

    Article  ADS  Google Scholar 

Download references

Acknowledgements

The authors would like to thank S Bhattacharyya for useful discussion. SM would like to thank ICTS-TIFR for hospitality under the associateship programme where a part of this work had been done. Work of PPP was supported in part by UGC-BRS fellowship, Government of India.

Author information

Authors and Affiliations

  1. Department of Physics, Utkal University, Bhubaneswar,  751 004, India

    Priyanka Priyadarshini Pruseth & Swapna Mahapatra

Authors
  1. Priyanka Priyadarshini Pruseth
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Swapna Mahapatra
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Swapna Mahapatra.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Pruseth, P.P., Mahapatra, S. Anisotropic expansion, second-order hydrodynamics and holographic dual. Pramana - J Phys 95, 105 (2021). https://doi.org/10.1007/s12043-021-02133-w

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s12043-021-02133-w

Keywords

PACS Nos

Search

Navigation