# Evolutions of centered Brill waves with a pseudospectral method

## TL;DR

This paper uses a pseudospectral method to evolve Brill wave initial data, analyzing horizon formation and scalar curvature behavior, revealing coordinate effects and near-critical phenomena in gravitational wave evolution.

## Contribution

It provides a detailed numerical study of Brill wave evolutions, demonstrating control over apparent horizon formation and scalar curvature peaks, with insights into coordinate effects and near-critical behavior.

## Key findings

- Some subcritical amplitudes form apparent horizons.
- Peak of Kretschmann scalar can be controlled via slicing conditions.
- Evidence of power-law scaling with periodic wiggle near criticality.

## Abstract

The pseudospectral code bamps is used to evolve axisymmetric gravitational waves. We consider a one-parameter family of Brill wave initial data, taking the seed function and strength parameter of Holz et. al. A careful comparison is made to earlier work. Our results are mostly in agreement with the literature, but we do find that some amplitudes reported elsewhere as subcritical evolve to form apparent horizons. Related to this point we find that by altering the slicing condition, the position of the peak of the Kretschmann scalar in these supercritical data can be controlled so that it appears away from the symmetry axis before the method fails, demonstrating that such behavior is at least partially a coordinate effect. We are able to tune the strength parameter to an interval of range $1-A_\star/A\simeq10^{-6}$ around the onset of apparent horizon formation. In this regime we find that large spikes appear in the Kretschmann scalar on the symmetry axis but away from the origin. From the supercritical side disjoint apparent horizons form around these spikes. On the subcritical side, down to this range, evidence of power-law scaling of the Kretschmann scalar is not conclusive, but the data can be fitted as a power-law with periodic wiggle.