6533b855fe1ef96bd12b0891

RESEARCH PRODUCT

A scenario for critical scalar field collapse in $AdS_3$

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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 $\alpha0$ 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.