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

TL;DR

This paper extends the fluid/gravity duality framework by applying Petrov-like boundary conditions to spacetimes with a cosmological constant, deriving Navier-Stokes equations from black brane and curved backgrounds.

Contribution

It demonstrates that Petrov type I boundary conditions can be used to derive fluid dynamics equations in spacetimes with a cosmological constant, broadening the scope of the duality.

Findings

Navier-Stokes equations derived from black brane and curved spacetimes

Petrov boundary condition approach is consistent with hydrodynamical expansion

Framework applicable to spacetimes with cosmological constant

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.