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Journal Article

Crushing singularities in spacetimes with spherical, plane and hyperbolic symmetry


Rendall,  Alan D.
Geometric Analysis and Gravitation, AEI-Golm, MPI for Gravitational Physics, Max Planck Society;

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Rendall, A. D. (1995). Crushing singularities in spacetimes with spherical, plane and hyperbolic symmetry. Classical and Quantum Gravity, 12(6), 1517-1533.

Cite as: http://hdl.handle.net/11858/00-001M-0000-0013-5B9F-0
It is shown that the initial singularities in spatially compact spacetimes with spherical, plane or hyperbolic symmetry admitting a symmetric 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.