FLUID-GRAVITY CORRESPONDENCE UNDER THE PRESENCE OF VISCOSITY

Abstract

This work addresses the analogy between the speed of sound of a viscous, barotropic, and irrotational fluid and the equation of motion for a non-massive field in a curved manifold. It will be shown that the presence of viscosity implies the introduction, into the equation of motion of the gravitational analogue, of a source term which entails the flow of energy from the non-massive field to the curvature of the spacetime manifold. The stress–energy tensor is also computed and it is found not to be constant, which is consistent with such energy interchange.