Critical Parameterisation of the Brill Wave Initial Value Problem

A numerical framework to explore the Brill Wave Initial Value Problem is presented along with a review of some of the theoretical predictions concerning Brill waves. It is demonstrated that there is an agreement between the numerically observed phenomena and theory, namely that the IVP parameterisation of the metric function $q$ has a minimum and maximum amplitude for which a solution to the Hamiltonian for the metric function $phi$ exists, and a critical regime in the middle for which there are and are not apparent horizons present.