A scenario for critical scalar field collapse in AdS3
Abstract
We present a family of exact solutions, depending on two parameters α and b (related to the scalar field strength), to the three-dimensional Einstein-scalar field equations with negative cosmological constant Λ. For b = 0 these solutions reduce to the static Bañados-Teitelboim-Zanelli (BTZ) family of vacuum solutions, with mass $M=-\alpha $ M = - α . For $b\ne 0$ b ≠ 0 , the solutions become dynamical and develop a strong spacelike central singularity. The $\alpha \lt 0$ α < 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 $\alpha \gt 0$ α > 0 agrees qualitatively with that observed in numerical simulations of sub-critical collapse, including the independence of the near-critical regime on the angle deficit of the spacetime. We analyze in the $\Lambda =0$ Λ = 0 approximation the linear perturbations of the self-similar threshold solution, $\alpha =0$ α = 0 , and find that it has only one unstable growing mode, which qualifies it as a candidate critical solution for scalar field collapse.
- Publication:
-
Classical and Quantum Gravity
- Pub Date:
- May 2015
- DOI:
- 10.1088/0264-9381/32/9/095009
- arXiv:
- arXiv:1404.0589
- Bibcode:
- 2015CQGra..32i5009C
- Keywords:
-
- critical collapse;
- exact solutions;
- $Ad{{S}_{3}}$ AdS 3;
- General Relativity and Quantum Cosmology;
- High Energy Physics - Theory
- E-Print:
- 19 pages, 3 figures, revised version to be published in Class. Quant. Grav