Weak Field Black Hole Formation in Asymptotically AdS Spacetimes

TL;DR

This paper uses the AdS/CFT correspondence to analyze how strongly coupled conformal field theories thermalize under small, time-dependent perturbations, revealing rapid black hole formation or scattering depending on parameters.

Contribution

It introduces a systematic gravitational description of thermalization in AdS/CFT with arbitrary time-dependent sources, including a new connection to Choptuik scaling.

Findings

Rapid, scale-dependent thermalization process observed.

Black hole formation corresponds to plasma phase in boundary theory.

Transition between scattering and collapse can be tuned to Choptuik scaling.

Abstract

We use the AdS/CFT correspondence to study the thermalization of a strongly coupled conformal field theory that is forced out of its vacuum by a source that couples to a marginal operator. The source is taken to be of small amplitude and finite duration, but is otherwise an arbitrary function of time. When the field theory lives on $R^{d-1,1}$, the source sets up a translationally invariant wave in the dual gravitational description. This wave propagates radially inwards in $AdS_{d+1}$ space and collapses to form a black brane. Outside its horizon the bulk spacetime for this collapse process may systematically be constructed in an expansion in the amplitude of the source function, and takes the Vaidya form at leading order in the source amplitude. This solution is dual to a remarkably rapid and intriguingly scale dependent thermalization process in the field theory. When the field theory lives on a sphere the resultant wave either slowly scatters into a thermal gas (dual to a glueball type phase in the boundary theory) or rapidly collapses into a black hole (dual to a plasma type phase in the field theory) depending on the time scale and amplitude of the source function. The transition between these two behaviors is sharp and can be tuned to the Choptuik scaling solution in $R^{d,1}$.