Critical Parameterisation of the Brill Wave Initial Value Problem

TL;DR

This paper introduces a numerical framework to study the Brill Wave Initial Value Problem, confirming theoretical predictions about parameter ranges and horizon formation through computational experiments.

Contribution

It provides a new numerical approach to analyze the parameter space of Brill waves and validates theoretical predictions about solution existence and horizon formation.

Findings

Existence of minimum and maximum amplitude bounds for solutions.

Confirmation of a critical regime with horizon formation.

Agreement between numerical results and theoretical predictions.

Abstract

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.