Scalar field collapse in three-dimensional AdS spacetime

TL;DR

This paper presents a numerical study of scalar field collapse in three-dimensional Anti-de Sitter spacetime, demonstrating black hole formation and critical behavior near the threshold amplitude.

Contribution

It provides the first detailed numerical analysis of scalar collapse in 3D AdS spacetime, revealing critical phenomena and scaling laws for apparent horizon formation.

Findings

Black hole formation occurs when initial pulse amplitude exceeds a critical value.

Apparent horizon radius scales as (A - A_*)^{0.81} near criticality.

Evidence of critical phenomena in 3D AdS scalar collapse.

Abstract

We describe results of a numerical calculation of circularly symmetric scalar field collapse in three spacetime dimensions with negative cosmological constant. The procedure uses a double null formulation of the Einstein-scalar equations. We see evidence of black hole formation on first implosion of a scalar pulse if the initial pulse amplitude $A$ is greater than a critical value $A_*$. Sufficiently near criticality the apparent horizon radius $r_{AH}$ grows with pulse amplitude according to the formula $r_{AH} \sim (A-A_*)^{0.81}$.