# How does one convert the stress energy momentum tensor into a normal energy value?

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.

• Related question by the same OP: physics.stackexchange.com/q/523982 Jan 28 '20 at 6:57
• Some physical quantity, and the density of that quantity, are two different things. Think about mass density. You can have a little mass of a low-density substance, a lot of mass of low density, a little mass of high density, or a lot of mass of high density. So why do you expect some relationship between energy and energy density when you don’t specify the volume? Jan 28 '20 at 7:02
• If you specify, for example, a spherical mass of uniform density with some radius, you can calculate the metric tensor and the curvature tensor everywhere. Jan 28 '20 at 7:04
• en.wikipedia.org/wiki/Interior_Schwarzschild_metric Jan 28 '20 at 7:07
• If you want to chat, I have some time. Jan 28 '20 at 7:13

## 1 Answer

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.