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

TL;DR

The convergence radius of the formally obtained perturbative series is estimated and it is argued that it is greater then zero, which gives strong evidence for the nonlinear stability of the constructed time-periodic solutions.

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.

Figures (1)

• Figure 1: Visualization of the phase space generated by time evolution of initial data listed in Tab. \ref{['tab:initial_data']}. All plots depict the same solution evolved over time interval equal to 500 periods. Closed curves on the slices of phase space give a strong argument for the stability of analyzed solution.