Analytical approach to critical collapse in 2+1 dimensions

TL;DR

This paper introduces a family of self-similar solutions in 2+1 dimensional gravity with a scalar field, analyzing their stability and implications for black hole formation.

Contribution

It provides new time-dependent solutions with self-similarity in 2+1 gravity and investigates their linear perturbations and boundary conditions.

Findings

Identified two growing perturbation modes.

One mode relates to static singular solutions.

Another mode indicates black hole formation.

Abstract

We present a family of time-dependent solutions to 2+1 gravity with negative cosmological constant and a massless scalar field as source. These solutions are continuously self-similar near the central singularity. We analyze linear perturbations of these solutions, and discuss the subtle question of boundary conditions. We find two growing modes, one of which corresponds to the linearization of static singular solutions, while the other describes black hole formation.