Conformal symmetries of Einstein’s field equations and initial data

Abstract

This paper examines the initial data for the evolution of the space–time solution of Einstein’s equations admitting a conformal symmetry. Under certain conditions on the extrinsic curvature of the initial complete spacelike hypersurface and sectional curvature of the space–time with respect to sections containing the normal vector field, we have shown that the initial hypersurface is conformally diffeomorphic to a sphere or a flat space or a hyperbolic space or the product of an open real interval and a complete 2-manifold. It has been further shown that if the initial hypersurface is compact, then it is conformally diffeomorphic to a sphere. Finally, the conformal symmetries of a generalized Robertson–Walker space–time have been described.