Further consideration of energy and momentum in general relativity

Abstract

The problem of the proper formulation of the conservation laws of energy and linear momentum in general relativity is discussed. The Komar expression, taken as a generally covariant conservation law generator, is considered in light of the problem which Moller found with his energy-momentum complex. The conservation laws as formulated here from the Komar generator are shown to be devoid of such difficulties. Also, a generally covariant formulation of the conservation laws, which are differentiated from a covariant conservation-law generator, is effectively achieved without the necessity of introducing a tetrad structure. In this formulation the conservation lawsper se are noncovariant quantities; however, one may always return to the Komar generator and transform in a generally covariant manner any given conservation law, through its underlying symmetry representation, to any space-time co-ordinate system of interest. It is also possible, at least in some simple space-time systems, to formulate the energy and momentum when they are not rigorously conserved entities. Such expressions can have possible application, for example, in radiating gravitational systems.