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

Recently it has been shown that imposing Petrov-like condition on the boundary may reduce the Einstein equation to the Navier-Stokes equation in the nonrelativistic 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-like condition on the boundary should be equivalent to the conventional meühod using the hydrodynamical expansion of the metric in the near-horizon limit. [ABSTRACT FROM AUTHOR]