Fluid/gravity correspondence for massive gravity

TL;DR

This paper explores how massive gravity influences the fluid/gravity correspondence, showing that bulk perturbations obey Navier-Stokes equations on a boundary surface and that viscosity bounds are preserved.

Contribution

It extends the fluid/gravity correspondence to massive Einstein gravity, demonstrating the governing equations and viscosity bounds in this framework.

Findings

Bulk perturbations follow Navier-Stokes equations.

Viscosity to entropy ratio saturates the KSS bound.

Massive gravity effects are captured by effective energy-momentum tensor.

Abstract

In this paper, we investigate the fluid/gravity correspondence in the framework of massive Einstein gravity. Treating the gravitational mass terms as an effective energy-momentum tensor and utilizing the Petrov-like boundary condition on a timelike hypersurface, we find that the perturbation effects of massive gravity in bulk can be completely governed by the incompressible Navier-Stokes equation living on the cutoff surface under the near horizon and nonrelativistic limits. Furthermore, we have concisely computed the ratio of dynamical viscosity to entropy density for two massive Einstein gravity theories, and found that they still saturate the Kovtun-Son-Starinets (KSS) bound.