Generalized Navier–Stokes equations and soft hairy horizons in fluid/gravity correspondence

Abstract

The fluid/gravity correspondence establishes how gravitational dynamics, as dictated by Einstein's field equations, are related to the fluid dynamics, governed by the relativistic Navier–Stokes equations. In this work the correspondence is extended, where the duality between incompressible fluids and gravitational backgrounds with soft hair excitations is implemented. This construction is set through appropriate boundary conditions to the gravitational background, leading to a correspondence between generalized incompressible Navier–Stokes equations and soft hairy horizons.