Critical scalar field collapse in AdS_3: an analytic approach

TL;DR

This paper analytically investigates scalar field collapse in three-dimensional anti-de Sitter space, revealing critical behavior and scaling laws for horizon formation and black hole mass near the threshold parameter.

Contribution

It provides an exact analytical solution for scalar collapse in AdS_3 and identifies critical scaling laws for horizon radius and black hole mass.

Findings

Horizon forms when parameter p > 1

Horizon radius scales as (p-1)^(1/4)

Black hole mass scales as (p-1)^(1/2)

Abstract

We present an analytical solution of a massless scalar field collapsing in a three dimensional space-time with a negative cosmological constant, i.e. asymptotically AdS_3. The Einstein and scalar field equations are formulated using double null Poincare coordinates. Trapping horizons form when a critical parameter is p > 1. There are indications that the horizon radius r_AH scales like r_AH ~ (p-1)^(1/4) and the black hole mass as M ~ r_AH^2 ~ (p-1)^(1/2), i.e. with a critical mass exponent of 1/2.