SPECIAL CONFORMAL-SYMMETRIES IN GENERAL-RELATIVITY

A geometrical discussion of special conformal vector fields in space-time is given. In particular, it is shown that if such a vector field ξ is admitted, it is unique up to a constant scaling and the addition of a homothetic or a Killing vector field. In the case when the gradient of the conformal scalar associated with ξ is non-null it is shown that other homothetic and affine symmetries are necessarily admitted by the space-time, that an intrinsic family of 2-dimensional flat submanifolds is determined in the space-time, that ξ is, in general, hypersurface orthogonal and that the space-time, if non-flat, is necessarily (geodesically) incomplete. Other geometrical features of such space-times are also considered. © 1990 Plenum Publishing Corporation.