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Journal Article

#### Globally Regular Instability of 3-Dimensional Anti–De Sitter Spacetime

##### MPS-Authors

Bizon,  Piotr
AEI-Golm, MPI for Gravitational Physics, Max Planck Society;

##### External Ressource
No external resources are shared
##### Fulltext (public)

1306.0317.pdf
(Preprint), 311KB

PRL111_041102.pdf
(Any fulltext), 382KB

##### Supplementary Material (public)
There is no public supplementary material available
##### Citation

Bizon, P., & Jałmużna, J. (2013). Globally Regular Instability of 3-Dimensional Anti–De Sitter Spacetime. Physical Review Letters, 111: 041102. doi:10.1103/PhysRevLett.111.041102.

Cite as: http://hdl.handle.net/11858/00-001M-0000-0015-149A-5
##### Abstract
We consider three-dimensional AdS gravity minimally coupled to a massless scalar field and study numerically the evolution of small smooth circularly symmetric perturbations of the $AdS_3$ spacetime. As in higher dimensions, for a large class of perturbations, we observe a turbulent cascade of energy to high frequencies which entails instability of $AdS_3$. However, in contrast to higher dimensions, the cascade cannot be terminated by black hole formation because small perturbations have energy below the black hole threshold. This situation appears to be challenging for the cosmic censor. Analysing the energy spectrum of the cascade we determine the width $\rho(t)$ of the analyticity strip of solutions in the complex spatial plane and argue by extrapolation that $\rho(t)$ does not vanish in finite time. This provides evidence that the turbulence is too weak to produce a naked singularity and the solutions remain globally regular in time, in accordance with the cosmic censorship hypothesis.