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From Petrov-Einstein to Navier–Stokes in spatially curved spacetime

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Abstract

We generalize the framework in arXiv:1104.5502 to the case that an embedding may have a non-vanishing intrinsic curvature. Directly employing the Brown-York stress tensor as the fundamental variables, we study the effect of finite perturbations of the extrinsic curvature while keeping the intrinsic metric fixed. We show that imposing a Petrov type I condition on the hypersurface geometry may reduce to the incompressible Navier–Stokes equation for a fluid moving in spatially curved spacetime in the near-horizon limit.

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References

  1. T. Damour, Quelques propriétés mécaniques, électromagnétiques, thermodynamiques et quantiques des trous noirs, Ph.D. thesis, Université Paris 6, Paris France (1979) [http://www.ihes.fr/∼damour/Articles/].

  2. T. Damour, Surface effects in black hole physics, in Proceedings of the Second Marcel Grossmann Meeting on General Relativity, R. Ruffini ed., North Holland, Amsterdam The Netherlands (1982).

    Google Scholar 

  3. R. Price and K. Thorne, Membrane viewpoint on black holes: properties and evolution of the stretched horizon, Phys. Rev. D 33 (1986) 915 [ INSPIRE].

    MathSciNet  ADS  Google Scholar 

  4. T. Jacobson, Thermodynamics of space-time: The Einstein equation of state, Phys. Rev. Lett. 75 (1995) 1260 [gr-qc/9504004] [ INSPIRE].

    Article  MathSciNet  ADS  MATH  Google Scholar 

  5. G. Policastro, D. Son and A. Starinets, The Shear viscosity of strongly coupled N = 4 supersymmetric Yang-Mills plasma, Phys. Rev. Lett. 87 (2001) 081601 [hep-th/0104066] [ INSPIRE].

    Article  ADS  Google Scholar 

  6. G. Policastro, D.T. Son and A.O. Starinets, From AdS/CFT correspondence to hydrodynamics, JHEP 09 (2002) 043 [hep-th/0205052] [ INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  7. P. Kovtun, D.T. Son and A.O. Starinets, Holography and hydrodynamics: Diffusion on stretched horizons, JHEP 10 (2003) 064 [hep-th/0309213] [ INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  8. A. Buchel and J.T. Liu, Universality of the shear viscosity in supergravity, Phys. Rev. Lett. 93 (2004) 090602 [hep-th/0311175] [ INSPIRE].

    Article  ADS  Google Scholar 

  9. N. Iqbal and H. Liu, Universality of the hydrodynamic limit in AdS/CFT and the membrane paradigm, Phys. Rev. D 79 (2009) 025023 [arXiv:0809.3808] [ INSPIRE].

    ADS  Google Scholar 

  10. S. Bhattacharyya, S. Minwalla and S.R. Wadia, The incompressible non-relativistic Navier–Stokes equation from gravity, JHEP 08 (2009) 059 [arXiv:0810.1545] [ INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  11. C. Eling, I. Fouxon and Y. Oz, The incompressible Navier–Stokes equations from membrane dynamics, Phys. Lett. B 680 (2009) 496 [arXiv:0905.3638] [ INSPIRE].

    MathSciNet  ADS  Google Scholar 

  12. I. Bredberg, C. Keeler, V. Lysov and A. Strominger, From Navier–Stokes to Einstein, arXiv:1101.2451 [ INSPIRE].

  13. T. Padmanabhan, Entropy density of spacetime and the Navier–Stokes fluid dynamics of null surfaces, Phys. Rev. D 83 (2011) 044048 [arXiv:1012.0119] [ INSPIRE].

    ADS  Google Scholar 

  14. I. Bredberg, C. Keeler, V. Lysov and A. Strominger, Wilsonian approach to fluid/gravity duality, JHEP 03 (2011) 141 [arXiv:1006.1902] [ INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  15. G. Compere, P. McFadden, K. Skenderis and M. Taylor, The holographic fluid dual to vacuum Einstein gravity, JHEP 07 (2011) 050 [arXiv:1103.3022] [ INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  16. R.-G. Cai, L. Li and Y.-L. Zhang, Non-relativistic fluid dual to asymptotically AdS gravity at finite cutoff surface, JHEP 07 (2011) 027 [arXiv:1104.3281] [ INSPIRE].

    Article  ADS  Google Scholar 

  17. C. Niu, Y. Tian, X.-N. Wu and Y. Ling, Incompressible Navier–Stokes equation from Einstein-Maxwell and Gauss-Bonnet-Maxwell theories, arXiv:1107.1430 [ INSPIRE].

  18. V. Lysov and A. Strominger, From Petrov-Einstein to Navier–Stokes, arXiv:1104.5502 [ INSPIRE].

  19. I. Bredberg and A. Strominger, Black holes as incompressible fluids on the sphere, arXiv:1106.3084 [ INSPIRE].

  20. T. Huang, Y. Ling, W. Pan, Y. Tian and X. Wu, Fluid/gravity duality with Petrov boundary condition in a spacetime with a cosmological constant, in preparation.

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Authors and Affiliations

  1. Center for Relativistic Astrophysics and High Energy Physics, Department of Physics, Nanchang University, Nanchang, 330031, China

    Tai-Zhuo Huang, Yi Ling & Wen-Jian Pan

  2. Institute of Mathematics, Academy of Mathematics and System Science, CAS, Beijing, 100190, China

    Yi Ling & Xiao-Ning Wu

  3. Hua Loo-Keng Key Laboratory of Mathematics, CAS, Beijing, 100190, China

    Yi Ling & Xiao-Ning Wu

  4. College of Physical Sciences, Graduate University of Chinese Academy of Sciences, Beijing, 100049, China

    Yu Tian

Authors
  1. Tai-Zhuo Huang
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  2. Yi Ling
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  3. Wen-Jian Pan
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  4. Yu Tian
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  5. Xiao-Ning Wu
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Correspondence to Tai-Zhuo Huang.

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ArXiv ePrint: 1107.1464

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Huang, TZ., Ling, Y., Pan, WJ. et al. From Petrov-Einstein to Navier–Stokes in spatially curved spacetime. J. High Energ. Phys. 2011, 79 (2011). https://doi.org/10.1007/JHEP10(2011)079

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  • DOI: https://doi.org/10.1007/JHEP10(2011)079

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