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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.

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  • $\begingroup$ Related question by the same OP: physics.stackexchange.com/q/523982 $\endgroup$ – G. Smith Jan 28 at 6:57
  • $\begingroup$ 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? $\endgroup$ – G. Smith Jan 28 at 7:02
  • $\begingroup$ 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. $\endgroup$ – G. Smith Jan 28 at 7:04
  • $\begingroup$ en.wikipedia.org/wiki/Interior_Schwarzschild_metric $\endgroup$ – G. Smith Jan 28 at 7:07
  • $\begingroup$ If you want to chat, I have some time. $\endgroup$ – G. Smith Jan 28 at 7:13
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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.

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