Apparent horizons in simplicial Brill wave initial data

TL;DR

This paper constructs and compares initial data for Brill wave metrics using Regge calculus and continuum methods, identifying the critical amplitude for apparent horizon formation with consistent results.

Contribution

It introduces a novel approach using Regge calculus for initial data construction and verifies the critical amplitude for horizon formation.

Findings

Excellent agreement between Regge and continuum solutions.

Identification of a critical gravitational wave amplitude for apparent horizon formation.

Supports recent findings on horizon formation thresholds.

Abstract

We construct initial data for a particular class of Brill wave metrics using Regge calculus, and compare the results to a corresponding continuum solution, finding excellent agreement. We then search for trapped surfaces in both sets of initial data, and provide an independent verification of the existence of an apparent horizon once a critical gravitational wave amplitude is passed. Our estimate of this critical value, using both the Regge and continuum solutions, supports other recent findings.