General Covariant Conservation Law of Angular Momentum in General Relativity

The conservative Noether current corresponding to the invariance of the action of a gravitymatter system under the local Lorentz transformation can be interpreted as the angular momentum tensor of the system. The existence of superpotentials which are expressed in terms of the vierbein only makes the totd current iden ticdy conserved and the total angular momentum gauge-covariant. Two examples are given. It is shown that this conservation law of angular momentum in general relativity is reasonable.