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

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.

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Item Permalink: http://hdl.handle.net/11858/00-001M-0000-0015-149A-5 Version Permalink: http://hdl.handle.net/11858/00-001M-0000-0015-149B-3
Genre: Journal Article
Other : Globally regular instability of AdS_3

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1306.0317.pdf (Preprint), 311KB
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 Creators:
Bizon, Piotr1, Author
Jałmużna, Joanna, Author
Affiliations:
1AEI-Golm, MPI for Gravitational Physics, Max Planck Society, Golm, DE, escidoc:24008              

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Free keywords: General Relativity and Quantum Cosmology, gr-qc,High Energy Physics - Theory, hep-th,Mathematics, Analysis of PDEs, math.AP
 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.

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 Dates: 2013-06-032013
 Publication Status: Published in print
 Pages: 5 pages, 4 figures. Dedicated to Professor Andrzej Staruszkiewicz on the occasion of the 50th anniversary of his pioneering work on three-dimensional gravity
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 Table of Contents: -
 Rev. Method: -
 Identifiers: arXiv: 1306.0317
DOI: 10.1103/PhysRevLett.111.041102
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Title: Physical Review Letters
  Other : Phys. Rev. Lett.
Source Genre: Journal
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Publ. Info: Woodbury, N.Y. : American Physical Society
Pages: - Volume / Issue: 111 Sequence Number: 041102 Start / End Page: - Identifier: ISSN: 0031-9007
CoNE: http://pubman.mpdl.mpg.de/cone/journals/resource/954925433406_1