Approximately self-similar critical collapse in 2+1 dimensions

TL;DR

This paper investigates the critical collapse of a scalar field in 2+1 dimensions with negative cosmological constant, extending self-similar solutions and analyzing their perturbations to better understand black hole formation.

Contribution

It extends self-similar solutions to include negative cosmological constant and analyzes their linear perturbations, providing insights into critical collapse in lower-dimensional gravity.

Findings

Extended solutions characterized by a continuous parameter.

Parameter choice improves agreement with numerical results.

Studied the dynamics of the apparent horizon.

Abstract

Critical collapse of a self-gravitating scalar field in a (2+1)-dimensional spacetime with negative cosmological constant seems to be dominated by a continuously self-similar solution of the field equations without cosmological constant. However, previous studies of linear perturbations in this background were inconclusive. We extend the continuously self-similar solutions to solutions of the field equations with negative cosmological constant, and analyse their linear perturbations. The extended solutions are characterized by a continuous parameter. A suitable choice of this parameter seems to improve the agreement with the numerical results. We also study the dynamics of the apparent horizon in the extended background.