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Globally regular instability of 3-dimensional anti-de Sitter spacetime

Tuesday 17th September 2013 - 11:00 to 11:45
INI Seminar Room 1
Co-author: Joanna Jalmuzna (Jagiellonian University (Krakow))

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. We give evidence that the turbulence is too weak to produce a naked singularity and the evolution is globally regular in time, in accordance with the cosmic censorship hypothesis.
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Presentation Material: 
University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons