# Comment on ‘AdS nonlinear instability: moving beyond spherical symmetry’ (2016 Class. Quantum Grav. 33 23LT01 )

@article{Rostworowski2017CommentO, title={Comment on ‘AdS nonlinear instability: moving beyond spherical symmetry’ (2016 Class. Quantum Grav. 33 23LT01 )}, author={Andrzej Rostworowski}, journal={Classical and Quantum Gravity}, year={2017}, volume={34}, pages={128001} }

We argue that if the degeneracy of the spectrum of linear perturbations of AdS is properly taken into account, there are globally regular, time-periodic, asymptotically AdS solutions (geons) bifurcating from each linear eigenfrequency of AdS.

## 13 Citations

Anti–de Sitter geon families

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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…

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Being a key ingredient of the AdS/CFT correspondence, AdS space-time is suspected to be non-linearly unstable since 2011. Even with arbitrarily small initial data, a singularity almost invariably…

Fast and slow coherent cascades in anti-de Sitter spacetime

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We study the phase and amplitude dynamics of small perturbations in 3 + 1 dimensional anti-de Sitter spacetime using the truncated resonant approximation, also known as the two time framework. We…

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We report on numerical constructions of fully non-linear geons in asymptotically anti-de Sitter (AdS) spacetimes in four dimensions. Our approach is based on 3 + 1 formalism and spectral methods in…

Gravitational perturbations in a cavity: Nonlinearities

- PhysicsPhysical Review D
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Motivated by recent studies of nonlinear perturbations of asymptotically anti-de Sitter spacetimes, we study gravitational perturbations of $(n+2)$ dimensional Minkowski spacetime with a spherical…

The instability of anti-de Sitter space-time

- Physics
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In this review, we retrace the recent progress in the anti-de Sitter (AdS) instability problem. By instability we mean that for large classes of initial data, any perturbation of AdS space-time,…

Black resonators and geons in AdS
5

- PhysicsClassical and Quantum Gravity
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We construct dynamical black hole solutions with a helical symmetry in AdS$_5$, called black resonators, as well as their horizonless limits, called geons. We introduce a cohomogeneity-1 metric…

Localized Objects Formed by Self-Trapped Gravitational Waves

- PhysicsAstronomy Reports
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Geons are localized horizonless objects formed by gravitational waves, held together by the gravitational attraction of their own field energy. In many respects they are similar to scalar field…

Mathematical general relativity

- PhysicsGeneral Relativity and Gravitation
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We present a number of open problems within general relativity. After a brief introduction to some technical mathematical issues and the famous singularity theorems, we discuss the cosmic censorship…

A review on radiation of oscillons and oscillatons

- Physics
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Numerical simulations show that a massive real scalar field in a nonlinear theory can form long-lived oscillating localized states. For a self-interacting scalar on a fixed background these objects…

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Weakly turbulent instability of anti-de Sitter spacetime.

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The results suggest that AdS space is unstable under arbitrarily small generic perturbations, and it is conjecture that this instability is triggered by a resonant mode mixing which gives rise to diffusion of energy from low to high frequencies.

AdS nonlinear instability: moving beyond spherical symmetry

- Physics
- 2016

Anti-de Sitter (AdS) is conjectured to be nonlinear unstable to a weakly turbulent mechanism that develops a cascade towards high frequencies, leading to black hole formation [1,2]. We give evidence…

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

- Physics, MathematicsPhysical review letters
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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.