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.

arXiv comment65 pages, minor changes

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• Towards a theory of nonlinear gravitational waves: a systematic approach to nonlinear gravitational perturbations in vacuum
• Multioscillating black holes
• Superradiant instability of black resonators and geons
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• Freely falling bodies in a standing-wave spacetime
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• Gravitational Perturbations in a cavity: Nonlinearities
• Asymptotically Anti-de Sitter Spherically Symmetric Hairy Black Holes