Collapse of a Scalar Field in 2+1 Gravity

TL;DR

This paper investigates the critical gravitational collapse of a scalar field in 2+1 dimensions, analyzing self-similar solutions and their perturbations to identify the critical solution and compare it with numerical results.

Contribution

It provides an analytic study of self-similar solutions and their perturbations, identifying a critical solution that closely matches numerical findings in 2+1 gravity.

Findings

Identified a critical solution with a single unstable mode.

Found a critical exponent that differs from numerical results.

Analyzed global structure of self-similar solutions.

Abstract

We consider the problem of critical gravitational collapse of a scalar field in 2+1 dimensions with spherical (circular) symmetry. After surveying all the analytic, continuously self-similar solutions and considering their global structure, we examine their perturbations with the intent of understanding which are the critical solutions with a single unstable mode. The critical solution which we find is the one which agrees most closely with that found in numerical evolutions. However, the critical exponent which we find does not seem to agree with the numerical result.