The Petrov-like boundary condition at finite cutoff surface in Gravity/Fluid duality

TL;DR

This paper extends the gravity/fluid duality by demonstrating that Petrov-like boundary conditions at any finite cutoff surface, not just near the horizon, can lead to the Navier-Stokes equation using a non-relativistic long-wavelength limit.

Contribution

It generalizes previous near-horizon results to arbitrary finite cutoff surfaces, broadening the applicability of the gravity/fluid duality framework.

Findings

Navier-Stokes equation derived at finite cutoff surface

Extension of Petrov-like boundary condition approach beyond near horizon

Validation using non-relativistic long-wavelength limit

Abstract

Previously it has been shown that imposing a Petrov-like boundary condition on a hypersurface may reduce the Einstein equation to the incompressible Navier-Stokes equation, but all these correspondences are established in the near horizon limit. In this note, we remark that this strategy can be extended to an arbitrary finite cutoff surface which is spatially flat, and the Navier-Stokes equation is obtained by employing a non-relativistic long-wavelength limit.