Holographic fluid from nonminimally coupled scalar-tensor theory of gravity

We establish the gravity/fluid correspondence in the nonminimally coupled scalar-tensor theory of gravity. Imposing Petrov-like boundary conditions over the gravitational field, we find that, for a certain class of background metrics, the boundary fluctuations obey the standard Navier-Stokes equation for an incompressible fluid without any external force term in the leading order approximation under the near horizon expansion. That is to say, the scalar field fluctuations does not contribute in the leading order approximation regardless of what kind of boundary condition we impose on it.