Phase Diagram of Stability for Massive Scalars in Anti-de Sitter Spacetime

TL;DR

This paper maps the stability regions of massive scalar fields in 5D anti-de Sitter spacetime, revealing how mass influences stability, metastability, and chaotic collapse behaviors.

Contribution

It provides the first comprehensive phase diagram of stability for massive scalars in AdS, including nonperturbative and chaotic phenomena.

Findings

Increased scalar mass enlarges the stable initial data region.

Metastable data can form horizons over longer times than perturbation theory predicts.

Chaotic behavior observed in massless scalar collapse.

Abstract

We diagram the behavior of 5-dimensional anti-de Sitter spacetime against horizon formation in the gravitational collapse of a scalar field, treating the scalar field mass and width of initial data as free parameters, which we call the stability phase diagram. We find that the class of stable initial data becomes larger and shifts to smaller widths as the field mass increases. In addition to classifying initial data as stable or unstable, we identify two other classes based on nonperturbative behavior. The class of metastable initial data forms a horizon over longer time scales than suggested by the lowest order perturbation theory at computationally accessible amplitudes, and irregular initial data can exhibit non-monotonic and possibly chaotic behavior in the horizon formation times. Our results include evidence for chaotic behavior even in the collapse of a massless scalar field.