Anti-de Sitter geon families

Abstract

A detailed perturbative construction of globally regular, asymptotically anti-de Sitter (AdS) time-periodic solutions of Einstein's equations with a negative cosmological constant (AdS geons) is presented. Starting with the most general superposition of the $l=2$ even parity (scalar) eigenmodes of AdS at linear order, it is shown that at the fifth order in perturbation theory one obtains five one-parameter geon families, two of which have a helical Killing vector, one with axial symmetry, and two others without continuous symmetries. The details and some subtle aspects of the perturbative expansions are also presented.

65 pages, minor changes

References in corpus (7)

• Renormalization group, secular term resummation and AdS (in)stability
• Collapse and Nonlinear Instability of AdS with Angular Momenta
• Asymptotically anti-de Sitter Proca Stars
• Non-Spherically Symmetric Collapse in Asymptotically AdS Spacetimes
• Towards a theory of nonlinear gravitational waves: a systematic approach to nonlinear gravitational perturbations in vacuum
• Time-periodic solutions of massive scalar fields in AdS background: perturbative constructions
• The instability of anti-de Sitter space-time

Cited by in corpus (4)

• Towards a theory of nonlinear gravitational waves: a systematic approach to nonlinear gravitational perturbations in vacuum
• Superradiant instability of black resonators and geons
• A review on radiation of oscillons and oscillatons
• The instability of anti-de Sitter space-time