1111.1576 (Tai-Zhuo Huang et al.)

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

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

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.

View original: http://arxiv.org/abs/1111.1576