A scenario for critical scalar field collapse in $Ad{S}_3$

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 $b\ne 0$, 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.

19 pages, 3 figures, revised version to be published in Class. Quant. Grav

References in corpus (1)

• Critical scalar field collapse in AdS_3: an analytic approach

Cited by in corpus (2)

• Quasinormal modes of charged BTZ black holes
• Unveiling horizons in quantum critical collapse