Position space analysis of the AdS (in)stability problem

TL;DR

This paper analyzes the stability of global AdS space under small perturbations, using position space methods to understand the conditions under which collapse to black holes occurs or is avoided, and explores implications for holographic thermalization.

Contribution

It introduces a position space analysis of AdS stability, providing new insights into the dynamics of perturbations and the conditions for black hole formation.

Findings

Gravitational self-interactions cause tidal effects that can focus or defocus energy.

A nonzero measure of initial conditions do not lead to collapse within the gravitational time scale.

The formalism clarifies the link between AdS evolution and holographic thermalization.

Abstract

We investigate whether arbitrarily small perturbations in global AdS space are generically unstable and collapse into black holes on the time scale set by gravitational interactions. We argue that current evidence, combined with our analysis, strongly suggests that a set of nonzero measure in the space of initial conditions does not collapse on this time scale. We perform an analysis in position space to study this puzzle, and our formalism allows us to directly study the vanishing-amplitude limit. We show that gravitational self-interaction leads to tidal deformations which are equally likely to focus or defocus energy, and we sketch the phase diagram accordingly. We also clarify the connection between gravitational evolution in global AdS and holographic thermalization.