Crushing singularities in spacetimes with spherical, plane and hyperbolic symmetry

TL;DR

This paper proves that certain symmetric spacetimes with specific matter content inevitably develop crushing singularities at their initial points, extending understanding of singularity formation in general relativity.

Contribution

It demonstrates that spatially compact symmetric spacetimes with specific matter models always have crushing singularities, especially when certain geometric conditions are met.

Findings

Crushing singularities occur in these symmetric spacetimes with Vlasov or wave matter.

Existence of maximal slices implies crushing singularities both in past and future.

Matter models satisfy energy conditions and avoid singularities in regular backgrounds.

Abstract

It is shown that the initial singularities in spatially compact spacetimes with spherical, 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.