In the case of the Einstein field equations, is it possible to change from the stress energy momentum tensor into a normal energy value? Is it possible to say 'E =' instead of the Einstein constant multiplied by the SEM tensor?
This is in trying to find the curvature of spacetime in response to an object's energy/mass.
You can’t, because the energy-momentum tensor involves the energy density (and other things like the flow of energy, the density of momentum, and the flow of momentum). Energy density and energy are two different things.
Knowing just the energy of an object doesn’t give you enough information to solve Einstein’s field equations.
But if you know how the energy and momentum of a system are distributed and are flowing, then you can solve — sometimes analytically, sometimes numerically — the field equations for the metric tensor, and from that you can calculate all the components of the Riemann curvature tensor.
