 Indeed, since this is the case, observing that formula_38, we then have

We can then conclude that the terms of formula_40 represent the energy flux density of the system.Note that the trace is defined to be formula_41.Note that

When we use our formula for the stress–energy tensor found above,

Using the raising and lowering properties of the metric, and the fact that formula_44,

Since formula_46, so that we can conclude that

In general relativity, the symmetric stress–energy tensor acts as the source of spacetime curvature, and is the current density associated with gauge transformations of gravity which are general curvilinear coordinate transformations.