IRREDUCIBLE DECOMPOSITION OF EINSTEINS EQUATIONS IN SPACETIMES WITH SYMMETRIES

In this paper we develop a method to write Einstein's field equations for general matter in an irreducible form that fully incorporates the character of a symmetry introduced in spacetime. We express our method using the framework of double congruences and thus the formalism is c ovariant. The basic notion on which it is based is that of the geometr isation of a general symmetry. We apply our general scheme to the case of a spacelike conformal Killing vector field on the spacetime manifo ld regarding the situations of a perfect fluid and anisotropic matter. (C) 1998 Academic Press.