Simplicial Brill wave initial data

TL;DR

This paper develops a simplicial lattice approach using Regge calculus to generate initial data for vacuum axisymmetric Brill waves, demonstrating second-order accuracy in approximating continuum solutions.

Contribution

It introduces a tetrahedral lattice method tailored for axisymmetric Brill wave initial data, advancing numerical relativity techniques.

Findings

Only tetrahedral lattices successfully reproduce continuum solutions.

Constructed initial data are second order accurate approximations.

Applicable to both Brill waves and distorted black hole spacetimes.

Abstract

Regge calculus is used to construct initial data for vacuum axisymmetric Brill waves at a moment of time symmetry. We argue that only a tetrahedral lattice can successfully reproduce the continuum solution, and develop a simplicial axisymmetric lattice based on the co-ordinate structure of the continuum metric. This is used to construct initial data for Brill waves in an otherwise flat spacetime, and for the distorted black hole spacetime of Bernstein. These initial data sets are shown to be second order accurate approximations to the corresponding continuum solutions.