Can Newton gravitational constant be equal to Space curvature/stress energy momentum tensor?

Question

Is it correctly derived from Einstein's field equation?

Answer 1

no.
the stress-energy tensor tells us how the energy is spread, and moves, across spacetime.
the gravitational constant is a parameter that determines to what degree 1 kg of mass (for instance) will "warp" the spacetime.

so, you can't derive it from the einstein equation.

in fact, relativists usually set the gravitational constant to = 1, so that they don't have to deal with it. although it's essential when you're trying to determine exactly what your physical predictions will be, it's not really an active element of einstein's theory. it just kind of sits there.