Numerical study of some spherically symmetric and axisymmetric cosmological models

Two computer codes are described whose purpose is the study of inhomogeneous cosmological models. The first code assumes spherical symmetry, whereas the second is more general, assuming only axisymmetry. Both codes are based upon the 3 + 1 decomposition of Arnowitt, Deser, and Misner. With this approach, general relativity is cast into a dynamical form that has proved fruitful for numerical solution. The conformal approach of York is employed to solve the initial-value problem. Gauge conditions are set in order to write the three-metric in the simplest possible form. Constant-mean-curvature time slicing is used to determine the foliation of spacelike hypersurfaces. In the case of spherical symmetry, the three-metric is put into diagonal form. A fully-constrained evolution is performed. The code has full hydrodynamical capabilities. Outer boundary conditions are applied by requiring that the metric become the Friedmann-Robertson-Walker metric appropriate to the matter energy density at the edge of the computational mesh. The axisymmetric code is based upon a code developed by Wilson and Dykema and by Evans to treat the problem of nonspherical gravitational collapse in asymptotically-flat space times. Appropriate modifications were made to permit cosmological models to be studied