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}
}
  • A. Rostworowski
  • Published 30 November 2016
  • Mathematics, Physics
  • Classical and Quantum Gravity
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. 
Anti–de Sitter geon families
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
Gravitational systems in asymptotically anti-de Sitter space-times
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
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
Gravitational geons in asymptotically anti-de Sitter spacetimes
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
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
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
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
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
  • A. Coley
  • Physics
    General Relativity and Gravitation
  • 2019
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
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
...
1
2
...

References

SHOWING 1-3 OF 3 REFERENCES
Weakly turbulent instability of anti-de Sitter spacetime.
TLDR
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
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.
TLDR
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.