Abstract
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 covariant. The basic notion on which it is based is that of the geometrisation of a general symmetry. We apply our general scheme to the case of a spacelike conformal Killing vector field on the spacetime manifold regarding the situations of a perfect fluid and anisotropic matter.
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