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arXiv · 1404.0589

A scenario for critical scalar field collapse in $AdS_3$

Gérard Clément·Alessandro Fabbri
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Abstract

We present a family of exact solutions, depending on two parameters $\alpha$ and $b$ (related to the scalar field strength), to the three-dimensional Einstein-scalar field equations with negative cosmological constant $\Lambda$. For $b=0$ these solutions reduce to the static BTZ family of vacuum solutions, with mass $M = -\alpha$. For $b\neq0$, the solutions become dynamical and develop a strong spacelike central singularity. The $\alpha<0$ solutions are black-hole like, with a global structure topologically similar to that of the BTZ black holes, and a finite effective mass. We show that the near-singularity behavior of the solutions with $\alpha>0$ agrees qualitatively with that observed in numerical simulations of subcritical collapse. We analyze the linear perturbations of the threshold solution, $\alpha=0$, in the $\Lambda=0$ approximation, and find that it has only one unstable growing mode, which qualifies it as a candidate critical solution for scalar field collapse.

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Gérard Clément, Alessandro Fabbri. 2014-04-02. A scenario for critical scalar field collapse in $AdS_3$. https://doi.org/10.1088/0264-9381/32/9/095009

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