ENERGY-MOMENTUM CONSERVATION IN GRAVITY THEORIES

We discuss general properties of the conservation law associated with, a local symmetry. Using Noether's theorem and a generalized Belinfant e symmetrization procedure in 3+1 dimensions, a symmetric energy-momen tum (pseudo) tensor for the gravitational Einstein-Hilbert action is d erived and discussed in detail. In 2 + 1 dimensions, expressions are o btained for energy and angular momentum arising in the ISO(2,1) gauge- theoretical formulation of Einstein gravity. In addition, an expressio n for energy in a gauge-theoretical formulation of the string-inspired (1 + 1)-dimensional gravity is derived and compared with the ADM defi nition of energy.