CONSISTENCY OF THE FIELD EQUATIONS IN THE SCALE COVARIANT THEORY OF GRAVITATION

Abstract

In the theory of general relativity, it is well known that the integrability conditions for Einstein's field equations are the conservation equations. The latter guarantee that if the constraint equations G^oa = kT^oa hold on an initial surface, and if G^av = kT^av at all times, then the constraint equations will hold at all earlier and later times. This ensures the consistency of the field equations and underlies the initial value approach to their solution. We investigate the corresponding result in the scale co-variant theory of gravitation.