[saspinski (OP)]

The classical gravitation law can, at the surface of a spherical homogeneous body, be written as:
a = G*(4/3*π*r³)*μ / r² =  4/3*π*G*μ*r; and the divergence of the acceleration in spherical coordinates is: div a = 4*π*G*μ.
where μ is the body density and G the gravitational constant.
That divergence has units of 1/T². When comparing to the Gaussian expression for the curvature of the surface of the sphere: 1/R²,  there is a similarity. Is it only a coincidence or the GR measure of spacetime curvature for that geometry can be approximated, for small velocities and mass densities, by that expression?

[PmbPhy]

The classical gravitation law can, at the surface of a spherical homogeneous body, be written as:
a = G*(4/3*π*r³)*μ / r² =  4/3*π*G*μ*r; and the divergence of the acceleration in spherical coordinates is: div a = 4*π*G*μ.
where μ is the body density and G the gravitational constant.
That divergence has units of 1/T². When comparing to the Gaussian expression for the curvature of the surface of the sphere: 1/R²,  there is a similarity. Is it only a coincidence or the GR measure of spacetime curvature for that geometry can be approximated, for small velocities and mass densities, by that expression?

A coincidence. Spacetime cannot be specified by a single number. It's specified by a 4x4 tensor.

[jeffreyH]

Well I have some observations that I do not have time to post at the moment.