About the link between General Relativity and Navier Stokes equations

From geodesics equations, it is possible to calculate variations of scalar velocity vector field between two points M and M'. You will then obtain the absolute differential of velocity field along the geodesic curve. Building then easily the Riemann-Christoffel tensor, you obtain the well known Bianchi identity which will allow to build the famous general relativity equation of Einstein. This tensorial equation make the link between spacetime curvature and pressures included in the impulsion energy tensor.

In this complex mathematical procedure, it is not very easy to find a link with the famous Navier Stokes equation describing the flow of fluids. The solution is to be able to transform the Einstein equation in the same form than Navier-Stokes one. The secret is in the factor (c²/R^0.5) I introduced in my book.