Stress-energy tensor
The
stress-energy tensor is a
tensor quantity in
general relativity. It describes the flow of
energy and
momentum. It satisfies the
continuity equation
-
The quantity
-
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, and is the current density associated with gauge transformations (in this case coordinate transformations) by
Noether's theorem.
In curved spacetime, the spacelike integral now depends on the spacelike slice, in general. There is in fact no way to define a global energy-momentum vector in a general curved spacetime.
External links
- http://people.hofstra.edu/faculty/Stefan_Waner/diff_geom/Sec12.html