Conformal deformations, Ricci curvature and energy conditions on globally hyperbolic spacetimes

Globally hyperbolic spacetimes (M, g) of dimension >= 3 satisfying the curvature condition Ric (g) (v,v) > = 0 for all non-spacelike tangent vectors v in TM are considered. This curvature condition arises naturally as an energy condition in cosmology. Suppose (M,g) admits a smooth globally hyperbolic time function h:M → R such that for some tsub(O), the Cauchy surface h-(tsub(O)) satisfies the strict curvature condition Ric (g) (v,v) > O for all non-spacelike v attached to h-1 (tsub(O)). Then M admits a metric g' conformal to g satisfying the strict curvature condition Ric (g') (v,v) > O for all non-spacelike v in TM. If the curvature and strict curvature conditions are restricted to null vectors, the analogous result may be obtained. Similar results may also be obtained for the scalar curvature in dimension > = 2 and for non-positive Ricci curvature. (author)