Crushing singularities in spacetimes with spherical, plane and hyperbolic symmetry

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.Comment: 19 page

Matrix model superpotentials and . . .

We use F. Ferrari’s methods relating matrix models to Calabi–Yau spaces in order to explain much of Intriligator and Wecht’s ADE classifi-cation of N = 1 superconformal theories which arise as RG fixed points of N = 1 SQCD theories with adjoints. We find that ADE superpoten-tials in the Intriligator–Wecht classification exactly match matrix model superpotentials obtained from Calabi–Yau with corresponding ADE sin-gularities. Moreover, in the additional ̂O, ̂A, ̂D and ̂E cases we find new singular geometries. These “hat ” geometries are closely related to their ADE counterparts, but feature non-isolated singularities. As a byproduct, we give simple descriptions for small resolutions of Gorenstein threefold singularities in terms of transition functions between just two co-ordinate charts. To obtain these results we develop an algorithm for blowing down exceptional P1, described in the appendix. e-print archive