Fluid/Gravity duality with Petrov boundary condition in a spacetime with a cosmological constant

Details Fluid/Gravity duality with Petrov boundary condition in a spacetime with a cosmological constant Fluid/Gravity duality with Petrov boundary condition in a spacetime with a cosmological constant

2011-11-07

arxiv.org/abs/1111.1576v1

Physics

High Energy Physics

High Energy Physics - Theory

14 pages

Scientific paper

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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