Plane-symmetric cosmology with relativistic hydrodynamics

A numerical code, developed for cosmology and to investigate fully nonlinear behavior in the plane-symmetric Einstein equations, is described in detail. The field equations are solved self-consistently with the general relativistic hydrodynamical conservation equations, using artificial viscosity methods for shock capturing and an ideal fluid stress-energy tensor with a cosmological constant. Several tests of the code are presented, including anisotropically expanding vacuum and isotropically expanding de Sitter, dust-filled and radiation-filled cosmologies, gravitational waves in Bat and anisotropically expanding background models, sub- and super-horizon scale density perturbations in an expanding FLRW background, and both Newtonian and relativistic shock tube evolutions. Also discussed is a gauge drift instability that can appear in near-geodesic evolutions of density perturbations when the dynamical time scale of collapse becomes smaller than the cosmological expansion rate. [S0556-2821(98)00918-7].