over a spacelike slice gives the energy-momentum vector. This tensor is the Noether current associated with spacetimetranslations. In general relativity, this quantity acts as the source of spacetime curvature. One thing to note is that in curved spacetime, the spacelike integral now depends on the spacelike slice in general. This is simply the statement that there's no way to define a global energy-momentum vector in a general curved spacetime.
