What could we learn if we found the second moment of mass for a taurus and use E = mc2 to find second moment of energy?
We may be able to learn if a red rag has any effect ("taurus" means "bull") - perhaps you mean a "torus"? Sort of a doughnut shape? The second moment of mass is just the moment of inertia. So we know what that is. E=mc^2 would be the rest-mass energy of something. Just blindly substituting a rest-mass energy density for mass in the moment of inertia calculation will still get you the (non-relativistic) moment of inertia as before - just in different units.