Scalar Collapse in AdS

TL;DR

This paper investigates the gravitational collapse of a complex scalar field in AdS spacetime, confirming black hole formation from small initial data and exploring the energy transfer mechanisms involved.

Contribution

It extends previous scalar collapse studies to include complex fields and analyzes the effects of finite boundary conditions on black hole formation.

Findings

Black hole formation occurs even with a finite reflecting boundary.

Energy transfer to higher frequencies is crucial for collapse.

Collapse phenomena are intrinsic to gravity in bounded domains.

Abstract

Recently, studies of the gravitational collapse of a scalar field within spherically symmetric AdS spacetimes was presented in \cite{Bizon:2011gg,Jalmuzna:2011qw} which showed an instability of pure AdS to black hole formation. In particular, the work showed that arbitrarily small initial configurations of scalar field evolved through some number of reflections off the AdS boundary until a black hole forms. We consider this same system, extended to include a complex scalar field, and reproduce this phenomena. We present tests of our numerical code that demonstrate convergence and consistency. We study the properties of the evolution as the scalar pulse becomes more compact examining the asymptotic behavior of the scalar field, an observable in the corresponding boundary CFT. We demonstrate that such BH formation occurs even when one places a reflecting boundary at finite radius indicating that the sharpening is a property of gravity in a bounded domain, not of AdS itself. We examine how the initial energy is transferred to higher frequencies --which leads to black hole formation-- and uncover interesting features of this transfer.