Numerical evolution, linear and nonlinear, of spherically symmetric deviations from an isotropic universe

Abstract

We describe an algorithm for solving 1 + 1-systems that are in symmetric hyperbolic form. It is applied to spherically symmetric deviations from ak = 0, radiation filled Isotropic universe. We compare the solution to the full Einstein equations with those of the linearized equations. For small enough initial data the evolutions are indistinguishable. However, for large data, i.e., for initial density contrasts in the 1 percent range, trapped surfaces appear and singularities form.