On the Ricci curvature of compact spacelike hypersurfaces in Einstein conformally stationary-closed spacetimes
The purpose of this paper is to establish a sufficient condition for a compact spacelike hypersurface \(M\) in a spacetime \(\overline M\) equipped with a timelike closed conformal vector field \(K\), to be a leaf of the foliation determined by \(K\), in terms of a pinching condition for its Ricci curvature. With this aim, an integral formula involving the Ricci and scalar curvatures of the hypersurface \(M\) (being \(\overline M\) non necessarily Einstein) is developed, which furthermore allows one to obtain several non-existence results. Moreover, some interesting consequences for the particular case, when \(\overline M\) is a generalized Robertson-Walker spacetime, are obtained.
Einstein conformally stationary-closed spacetime
scientific article; zbMATH DE number 1915850
scientific article