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Novel Rotating Hairy Black Hole in (2+1)-Dimensions and Shear Viscosity to Entropy Ratio

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Abstract

The novel rotating hairy black hole metric in (2 + 1) dimensions, which is an exact solution to the field equations of the Einstein-scalar AdS theory with a non-minimal coupling, considered in this paper and some hydrodynamics quantities such as diffusion constant and shear viscosity investigated. By using thermodynamics quantities such as temperature and entropy we can use diffusion constant to obtain shear viscosity and then calculate shear viscosity to entropy ratio.

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References

  1. Xu, W., Zhao, L.: Charged black hole with a scalar hair in (2+1) dimensions. Phys. Rev. D87, 124008 (2013)

    ADS  Google Scholar 

  2. Zhao, L., Xu, W., Zhu, B.: Novel rotating hairy black hole in (2+1)-dimensions. arXiv:http://arxiv.org/abs/1305.6001 [gr-qc]

  3. Hortacsu, M., Ozcelik, H.T., Yapiskan, B.: Properties of solutions in 2+1 dimensions. Gen. Rel. Grav. 35, 1209 (2003)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  4. Henneaux, M., Martinez, C., Troncoso, R., Zanelli, J.: Black holes and asymptotics of 2+1 gravity coupled to a scalar field. Phys. Rev. D65, 104007 (2002)

    ADS  MathSciNet  Google Scholar 

  5. Hasanpour, M., Loran, F., Razaghian, H.: Gravity/CFT correspondence for three dimensional Einstein gravity with a conformal scalar field. Nucl. Phys. B867, 483 (2013)

    Article  ADS  MathSciNet  Google Scholar 

  6. Zeng, D.F.: An Exact Hairy Black Hole Solution for AdS/CFT Superconductors. arXiv:http://arxiv.org/abs/0903.2620 [hep-th]

  7. Chen, B., Xue, Z., ju Zhang, J.: Note on thermodynamic method of black hole/CFT correspondence. JHEP 1303, 102 (2013)

    Article  ADS  Google Scholar 

  8. Banados, M., Teitelboim, C., Zanelli, J.: The black hole in three-dimensional spacetime. Phys. Rev. Lett. 69, 1849 (1992)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  9. Sadeghi, J., Farahani, H., Pourhassan, B., Noorbakhsh, M.: Cosmic string in the BTZ black hole background with time-dependant tension. Phys. Lett. B 703, 14 (2011). arXiv:http://arxiv.org/abs/0903.0292 [hep-th]

    ADS  Google Scholar 

  10. Clement, G.: Classical solutions in three-dimensional Einstein-Maxwell cosmological gravity. Class. Quantum Grav. 10, L49 (1993)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  11. Clement, G.: Spinning charged BTZ black holes and self-dual particle-like solutions. Phys. Lett. B367, 70 (1996)

    Article  ADS  MathSciNet  Google Scholar 

  12. Martinez, C., Teitelboim, C., Zanelli, J.: Charged rotating black hole in three spacetime dimensions. Phys. Rev. D61, 104013 (2000)

    ADS  MathSciNet  Google Scholar 

  13. Sasaki, N., Miyamura, O., Muroya, S., Nonaka, C.: A calculation of baryon diffusion constant in hot and dense hadronic matter based on an event generator URASiMA. Phys. Rev. C62, 011901 (2000)

    ADS  Google Scholar 

  14. Sasaki, N., Miyamura, O., Muroya, S., Nonaka, C.: Baryon Diffusion Constant in Hot and Dense Hadronic Matter Based on an Event Generator Urasima. arXiv:http://arxiv.org/abs/hep-ph/0002019

  15. Sasaki, N., Miyamura, O., Muroya, S., Nonaka, C.: Charge diffusion constant in hot and dense hadronic matter - A Hadro-molecular-dynamic calculation. Europhys. Lett. 54, 38 (2001)

    Article  ADS  Google Scholar 

  16. Myers, R.C., Starinets, A.O., Thomson, R.M.: Holographic spectral functions and diffusion constants for fundamental matter. JHEP 0711, 091 (2007)

    Article  ADS  MathSciNet  Google Scholar 

  17. Shukla, A., Sharma, M., Mahesh, M.: Measurement of Translational Diffusion Constant using Noon State. arXiv:http://arxiv.org/abs/1110.1481 [quant-ph]

  18. Pang, D.-W.: Conductivity and diffusion constant in lifshitz backgrounds. JHEP 1001, 120 (2010)

    Article  ADS  Google Scholar 

  19. Sadeghi, J., Pourhassan, B., Amani, A.R.: The effect of higher derivative correction on η/s and conductivities in STU model. Int. J. Theor. Phys. 52, 42 (2013). arXiv:http://arxiv.org/abs/1011.2291 [hep-th]

    Article  MathSciNet  MATH  Google Scholar 

  20. Sadeghi, J., Chatrabhuti, A., Pourhassan, B.: Quasi-normal Modes of A d S 5 Black Hole at N=2 Supergravity. Int. J. Theor. Phys. 50, 129 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  21. J. Sadeghi, B. Pourhassan: Drag force of moving quark At N= 2 supergravity. JHEP 12, 026 (2008). arXiv:http://arxiv.org/abs/0809.2668 [hep-th]

    Article  ADS  MathSciNet  Google Scholar 

  22. Sadeghi, J., Setare, M.R., Pourhassan, B., Heshmatian, S.: Drag force of moving quark in STU background. Eur. Phys. J. C 61, 527 (2009). arXiv:http://arxiv.org/abs/0901.0217 [hep-th]

    Article  ADS  Google Scholar 

  23. Sadeghi, J., Setare, M.R., Pourhassan, B.: Drag force with different charges in STU background and AdS/CFT. J. Phys. G: Nucl. Part. Phys. 36, 115005 (2009). arXiv:http://arxiv.org/abs/0905.1466 [hep-th]

    Article  ADS  Google Scholar 

  24. Fadafan, K.B., Pourhassan, B., Sadeghi, J.: Calculating the jet-quenching parameter in STU background. Eur. Phys. J. C 71, 1785 (2011). arXiv:http://arxiv.org/abs/1005.1368 [hep-th]

    Article  ADS  Google Scholar 

  25. Pourhassan, B., Sadeghi, J.: STU/QCD correspondence. Can. J. Phys. 91, 995 (2013). arXiv:http://arxiv.org/abs/1205.4254 [hep-th]

    Article  ADS  Google Scholar 

  26. Pourhassan, B., Sadeghi, J., Chatrabhuti, A.: A d S 5 black hole at N=2 supergravity. Indian J. Phys. 87, 691 (2013). arXiv:http://arxiv.org/abs/0912.1423 [hep-th]

    Article  ADS  Google Scholar 

  27. Bu, Y.Y., Yang, J.M.: Spectral function and quark diffusion constant in non-critical holographic QCD. Nucl. Phys. B855, 388 (2012)

  28. Sadeghi, J., Pourhassan, B., Heshmatian, S.: Application of AdS/CFT in quark-gluon plasma. Adv. High Energy Phys. 2013, 759804 (2013)

    Article  MathSciNet  Google Scholar 

  29. Kontoudi, K., Policastro, G.: Diffusion constant of supercharge density in N=4 SYM at finite chemical potential. JHEP 1211, 044 (2012). arXiv:http://arxiv.org/abs/1206.2067 [hep-th]

    Article  ADS  Google Scholar 

  30. Policastro, G., Son, D.T., Starinets, A.O.: From AdS/CFT correspondence to hydrodynamics. JHEP 0209, 043 (2002). arXiv:http://arxiv.org/abs/hep-th/0205052

    Article  ADS  MathSciNet  Google Scholar 

  31. Kovtun, P., Son, D.T., Starinets, A.O.: Holography and hydrodynamics: diffusion on stretched horizons. JHEP 0310, 064 (2003). arXiv:http://arxiv.org/abs/hep-th/0309213

    Article  ADS  MathSciNet  Google Scholar 

  32. Buchel, A., Liu, J.T.: Universality of the shear viscosity in supergravity. Phys. Rev. Lett. 93, 090602 (2004). arXiv:http://arxiv.org/abs/hep-th/0311175

    Article  ADS  Google Scholar 

  33. Buchel, A., Myers, R.C., Paulos, M.F., Sinha, A.: Universal holographic hydrodynamics at finite coupling. Phys. Lett. B 669, 364 (2008). arXiv:http://arxiv.org/abs/0808.1837 [hep-th]

    Article  ADS  Google Scholar 

  34. Kovtun, P., Son, D.T., Starinets, A.O.: Viscosity in strongly interacting quantum field theories from black hole physics. Phys. Rev. Lett. 94, 111601 (2005). arXiv:http://arxiv.org/abs/hep-th/0405231

    Article  ADS  Google Scholar 

  35. Benincasa, P., Buchel, A.: Transport properties of N=4 supersymmetric Yang-Mills theory at finite coupling. JHEP 0601, 103 (2006). arXiv:http://arxiv.org/abs/hep-th/0510041

    Article  ADS  MathSciNet  Google Scholar 

  36. Saremi, O.: The viscosity bound conjecture and hydrodynamics of M2-brane theory at finite chemical Potential. JHEP 0610, 083 (2006). arXiv:http://arxiv.org/abs/hep-th/0601159

    Article  ADS  MathSciNet  Google Scholar 

  37. Kats, Y., Petrov, P.: Effect of curvature squared corrections in AdS on the viscosity of the dual gauge theory. JHEP 0901, 044 (2009). arXiv:http://arxiv.org/abs/0712.0743 [hep-th]

    Article  ADS  MathSciNet  Google Scholar 

  38. Myers, R.C., Paulos, M.F., Sinha, A.: Quantum corrections to η/s”. Phys. Rev. D 79, 041901 (2009). arXiv:http://arxiv.org/abs/0806.2156 [hep-th]

    Article  ADS  Google Scholar 

  39. Adams, A., Maloney, A., Sinha, A., Vazquez, S.E.: 1/N Effects in non-relativistic gauge-gravity duality. JHEP 0903, 097 (2009). arXiv:http://arxiv.org/abs/0812.0166 [hep-th]

    Article  ADS  MathSciNet  Google Scholar 

  40. Xian-Hui Ge, Sang-Jin Sin: Shear viscosity, instability and the upper bound of the Gauss-Bonnet coupling constant. JHEP 0905, 051 (2009). [arXiv:http://arxiv.org/abs/0903.2527 [hep-th]]

    Google Scholar 

  41. Ge, X.-H., Sin, S.-J., Wu, S.-F., Yang, G.-H.: Shear viscosity and instability from third order Lovelock gravity. Phys. Rev. D 80, 104019 (2009). arXiv:http://arxiv.org/abs/0905.2675 [hep-th]

    Article  ADS  Google Scholar 

  42. Ge, X.-H., Matsuo, Y., Shu, F.-W.: Visc osity bound, causality violation and instability with stringy correction and charge. JHEP 0810, 009 (2008). arXiv:http://arxiv.org/abs/0808.2354[hep-th]

    Article  ADS  MathSciNet  Google Scholar 

  43. Camanho, X.O., Edelstein, J.D.: Causality Constraints in AdS/CFT from Conformal Collider Physics and Gauss-Bonnet Gravity. arXiv:http://arxiv.org/abs/0911.3160 [hep-th]

  44. de Boer, J., Kulaxizi, M., Parnachev, A.: A d S 7/C F T 6, Gauss-Bonnet gravity, and viscosity bound. JHEP 1003, 097 (2010). arXiv:http://arxiv.org/abs/0910.5347 [hep-th]

    Google Scholar 

  45. Buchel, A., et al.: Holographic GB gravity in arbitrary dimensions. JHEP 1003, 111 (2010). arXiv:http://arxiv.org/abs/0911.4257 [hep-th]

    Article  ADS  Google Scholar 

  46. Shu, F.-W.: The quantum viscosity bound in lovelock gravity. Phys. Lett. B 685, 325 (2010). arXiv:http://arxiv.org/abs/0910.0607 [hep-th]

    Article  ADS  MathSciNet  Google Scholar 

  47. Camanho, X.O., Edelstein, J.D.: Causality in AdS/CFT and Lovelock Theory. arXiv:http://arxiv.org/abs/0912.1944 [hep-th]

  48. de Boer, J., Kulaxizi, M., Parnachev, A.: Holographic lovelock gravities and black holes. JHEP 1006, 008 (2010). arXiv:http://arxiv.org/abs/0912.1877 [hep-th]

    Article  ADS  MathSciNet  Google Scholar 

  49. Camanho, X.O., Edelstein, J.D., Paulos, M.F.: Lovelock theories, holography and the fate of the viscosity bound. JHEP 1105, 127 (2011). arXiv:http://arxiv.org/abs/1010.1682 [hep-th]

    Article  ADS  MathSciNet  Google Scholar 

  50. Belhaj, A., Chabab, M., EL Moumni, H., Sedra, M.B.: Critical Behaviors of 3D Black Holes with a Scalar Hair. arXiv:http://arxiv.org/abs/1306.2518 [hep-th]

  51. Ge, X.-H., Matsuo, Y., Shu, F.-W.: Viscosity Bound, causality violation and instability with stringy correction and charge. JHEP 0810, 009 (2008). arXiv:http://arxiv.org/abs/0808.2354[hep-th]

    Article  ADS  MathSciNet  Google Scholar 

  52. Camanho, X.O., Edelstein, J.D.: Causality constraints in AdS/CFT from conformal collider physics and Gauss-Bonnet gravity. JHEP 1004, 007 (2010). [arXiv:http://arxiv.org/abs/0911.3160 [hep-th]]

    Article  ADS  Google Scholar 

  53. de Boer, J., Kulaxizi, M., Parnachev, A.: A d S 7/C F T 6, Gauss-Bonnet gravity, and viscosity bound. JHEP 1003, 097 (2010). arXiv:http://arxiv.org/abs/0910.5347 [hep-th]

    Google Scholar 

  54. Sadeghi, J., Farahani, H.: Thermodynamics of a Charged Hairy Black Hole in (2+1) Dimensions. arXiv:http://arxiv.org/abs/1308.1054 [hep-th]

  55. Sadeghi, J., Pourhassan, B., Farahani, H.: Rotating Charged Hairy Black Hole in (2+1) Dimensions and Particle Acceleration. arXiv:http://arxiv.org/abs/1310.7142 [hep-th]

  56. Sadeghi, J., Pourhassan, B., Pourasadollah, F.: Holograghic Brownian Motion in 2+1 Dimensional Hairy Black Holes. arXiv:http://arxiv.org/abs/1312.4906 [hep-th]

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Naji, J., Heshmatian, S. Novel Rotating Hairy Black Hole in (2+1)-Dimensions and Shear Viscosity to Entropy Ratio. Int J Theor Phys 53, 2579–2586 (2014). https://doi.org/10.1007/s10773-014-2056-2

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