Time-periodic solutions in Einstein AdS - massless scalar field system

TL;DR

This paper constructs and analyzes time-periodic solutions in a self-gravitating massless scalar field system with negative cosmological constant, demonstrating their stability and relation to black hole formation.

Contribution

It provides the first combined perturbative and numerical construction of time-periodic solutions in Einstein-AdS with scalar fields, including convergence analysis and stability evidence.

Findings

Perturbative series have a positive convergence radius.

Numerical methods confirm the existence and stability of solutions.

Threshold for black-hole formation matches the convergence boundary.

Abstract

We construct time-periodic solutions for a system of self-gravitating massless scalar field, with negative cosmological constant, in d+1 spacetime dimensions at spherical symmetry, both perturbatively and numerically. We estimate the convergence radius of the formally obtained perturbative series and argue that it is greater then zero. Moreover, this estimate coincides with the boundary of the convergence domain of our numerical method and the threshold for the black-hole formation. Then we confirm our results with a direct numerical evolution. This also gives strong evidence for nonlinear stability of the constructed time-periodic solutions.