Crushing Singularities in Spacetimes with Spherical, Plane and HyperbolicSymmetry

摘要

It is shown that the initial singularities in spatially compact spacetimes withspherical, plane or hyperbolic symmetry admitting a compact constant mean curvature hypersurface are crushing singularities when the matter content of spacetime is described by the Vlasov equation (collisionless matter) or the wave equation (massless scalar field). In the spherically symmetric case, it is further shown that if the spacetime admits a maximal slice, then there are crushing singularities both in the past and in the future. The essential properties of the matter models chosen are that their energy-momentum tensors satisfy certain inequalities and that they do not develop singularities in a given regular background spacetime.