Scalar field breathers on anti-de Sitter background

Abstract

We study spatially localized, time-periodic solutions (breathers) of scalar field theories with various self-interacting potentials on Anti-de Sitter (AdS) spacetimes in $D$ dimensions. A detailed numerical study of spherically symmetric configurations in $D=3$ dimensions is carried out, revealing a rich and complex structure of the phase-space (bifurcations, resonances). Scalar breather solutions form one-parameter families parametrized by their amplitude, $\epsilon$, while their frequency, $\omega =\omega (\epsilon )$, is a function of the amplitude. The scalar breathers on AdS we find have a small amplitude limit, tending to the eigenfunctions of the linear Klein-Gordon operator on AdS. Importantly most of these breathers appear to be generically stable under time evolution.

30 pages, 22 figures

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• Time-periodic solutions of massive scalar fields in AdS background: perturbative constructions
• Self-Interacting Gravitational Atoms in the Strong-Gravity Regime
• A review on radiation of oscillons and oscillatons
• AdS nonlinear instability: breaking spherical and axial symmetries
• High precision numerical sequences of rotating hairy black holes
• Boundary conditions for stationary black holes ; Application to Kerr, Martinez-Troncoso-Zanelli and hairy black holes
• Dynamics of Nonlinear Waves on Bounded Domains
• Gravitational systems in asymptotically anti-de Sitter space-times
• Dynamics of a nonminimally coupled scalar field in asymptotically $Ad{S}_4$ spacetime