# Evolutions of Gowdy, Brill and Teukolsky initial data on a smooth lattice

## TL;DR

This paper demonstrates that a lattice method for computational general relativity can effectively evolve initial data for various space-times, matching results from existing methods and handling axisymmetric instabilities and boundary conditions well.

## Contribution

The paper introduces a lattice-based approach for evolving initial data in general relativity, showing its effectiveness for Brill, Teukolsky, and Gowdy space-times compared to traditional methods.

## Key findings

- Lattice method matches results from conventional techniques.
- Effective handling of axisymmetric instabilities.
- Good performance in wave passage through boundaries.

## Abstract

Numerical results, based on a lattice method for computational general relativity, will be presented for Cauchy evolution of initial data for the Brill, Teukolsky and polarised Gowdy space-times. The simple objective of this paper is to demonstrate that the lattice method can, at least for these space-times, match results obtained from contemporary methods. Some of the issues addressed in this paper include the handling of axisymmetric instabilities (in the Brill space-time) and an implementation of a Sommerfeld radiation condition for the Brill and Teukolsky space-times. It will be shown that the lattice method performs particularly well in regard to the passage of the waves through the outer boundary. Questions concerning multiple black-holes, mesh refinement and long term stability will not be discussed here but may form the basis of future work.