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arXiv · 1111.1576

Fluid/gravity duality with Petrov-like boundary condition in a spacetime with a cosmological constant

Tai-Zhuo Huang·Yi Ling·Wen-Jian Pan·Yu Tian·Xiao-Ning Wu
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Abstract

Recently it has been shown that imposing Petrov type I condition on the boundary may reduce the Einstein's equation to the Navier-Stokes equation in the non-relativistic and near-horizon limit. In this paper we extend this framework to a spacetime with a cosmological constant. By explicit construction we show that the Navier-Stokes equation can be derived from both black brane background and spatially curved spacetime. We also conjecture that imposing Petrov type I condition on the boundary should be equivalent to the conventional method using the hydrodynamical expansion of the metric in the near horizon limit.

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Tai-Zhuo Huang, Yi Ling, Wen-Jian Pan, Yu Tian, Xiao-Ning Wu. 2012-06-25. Fluid/gravity duality with Petrov-like boundary condition in a spacetime with a cosmological constant. https://doi.org/10.1103/physrevd.85.123531

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