Stress–energy–momentum pseudotensor: Difference between revisions

(→‎Definition: italic index variables)
# that it be index symmetric, i.e. <math>t_{LL}^{\mu \nu} = t_{LL}^{\nu \mu} \,</math>, (to conserve [[angular momentum]])
# that, when added to the [[stress–energy tensor]] of matter, <math>T^{\mu \nu}\,</math>, its total 4-[[divergence]] vanishes (this is required of any [[conserved current]]) so that we have a conserved expression for the total stress–energy–momentum.
# that it vanish locally in an [[inertial frame of reference]] (which requires that it only contains first and not second or higher [[derivative]]s of the metric). This is because the [[equivalence principle]] requires that the gravitational force field, the [[Christoffel symbols]], vanish locally in some frameframes. If gravitational energy is a function of its force field, as is usual for other forces, then the associated gravitational pseudotensor should also vanish locally.