The stress-energy tensor is a tensor quantity in relativity. It describes the flow of energy and momentum. It satisfies the continuity equation
over a spacelike slice gives the energy-momentum vector
. This tensor is the Noether current
associated with spacetime
translations. 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.