NUMERICAL INVESTIGATION OF COSMOLOGICAL SINGULARITIES

Although cosmological solutions to Einstein's equations are known to b e generically singular, little is known about the nature of singularit ies in typical spacetimes. It is shown here how the operator splitting used in a particular symplectic numerical integration scheme fits nat urally into the Einstein equations for a large class of cosmological m odels (whose dynamical variables are harmonic maps) and thus allows th e study of their approach to the singularity. The numerical method als o naturally singles out the asymptotically velocity term dominated (AV TD) behavior known to be characteristic of some of these models, conje ctured to describe others, and probably characteristic of a subclass o f the rest. The method is first applied to the generic (unpolarized) G owdy T3 cosmology. Exact pseudounpolarized solutions are used as a cod e test and demonstrate that a fourth-order accurate implementation of the numerical method yields acceptable agreement. For generic initial data, support for the conjecture that the singularity is AVTD with geo desic velocity (in the harmonic map target space) < 1 is found. A new phenomenon of the development of small scale spatial structure is also observed. Finally, it is shown that the numerical method straightforw ardly generalizes to an arbitrary cosmological spacetime on T3 X R wit h one spacelike U(1) symmetry.