Type II critical collapse on a single fixed grid: a gauge-driven ingoing boundary method

TL;DR

This paper introduces a simplified numerical method for gravitational collapse simulations that maintains a fixed grid by using gauge conditions, successfully reproducing key critical phenomena results.

Contribution

A novel gauge-driven boundary method that keeps the grid fixed during collapse simulations, simplifying the numerical approach compared to previous methods.

Findings

Successfully reproduces mass scaling and critical phenomena

Maintains a fixed grid without point removal or addition

Demonstrates effectiveness in spherical symmetry collapse

Abstract

We develop a numerical method suitable for gravitational collapse based on Cauchy evolution with an ingoing characteristic boundary. Unlike similar methods proposed recently (Ripley; Bieri, Garfinkle & Yau 2019/20), the numerical grid remains fixed during the evolution and no points need to be removed or added. Increasing coordinate refinement of the central region as the field collapses is achieved solely through the choice of spatial gauge and particularly its boundary condition. We apply this method to study critical collapse of a massless scalar field in spherical symmetry using maximal slicing and isotropic coordinates. Known results on mass scaling, discrete self-similarity and universality of the critical solution (Choptuik 1993) are reproduced using this considerably simpler numerical method.