Perturbations of an exact solution for 2+1 dimensional critical collapse

TL;DR

This paper analyzes the perturbation spectrum of self-similar solutions in 2+1 dimensional scalar field collapse, aiming to identify the critical solution by comparing theoretical predictions with numerical simulations.

Contribution

It computes the perturbation spectrum of exact CSS solutions in 2+1 dimensions and compares their stability properties to numerical critical collapse results.

Findings

Identifies a CSS solution with one unstable mode, potentially critical.

Finds another CSS solution with three unstable modes that better matches numerical data.

Highlights inconclusive evidence for the true critical solution.

Abstract

We find the perturbation spectrum of a family of spherically symmetric and continuously self-similar (CSS) exact solutions that appear to be relevant for the critical collapse of scalar field matter in 2+1 spacetime dimensions. The rate of exponential growth of the unstable perturbation yields the critical exponent. Our results are compared to the numerical simulations of Pretorius and Choptuik and are inconclusive: We find a CSS solution with exactly one unstable mode, which suggests that it may be the critical solution, but another CSS solution which has three unstable modes fits the numerically found critical solution better.