Fluid--Gravity Correspondence under the presence of viscosity

TL;DR

This paper explores how viscosity affects the fluid--gravity analogy, revealing that viscosity introduces energy exchange between the fluid's sound waves and the spacetime curvature, altering the gravitational analogue.

Contribution

It demonstrates that viscosity leads to a source term in the gravitational analogue's equation, indicating energy transfer and non-constant stress-energy tensor in the fluid--gravity correspondence.

Findings

Viscosity introduces a source term in the analogue gravity equations.

Energy flows from the fluid's sound mode to spacetime curvature.

The stress-energy tensor varies, reflecting energy exchange.

Abstract

The present 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.