PT Journal
AU Clement, G
   Fabbri, A
TI A scenario for critical scalar field collapse in AdS(3)
SO Classical and Quantum Gravity
JI Class. Quantum Gravity
PY 2015
BP 095009
EP 16pp
VL 32
IS 9
DI 10.1088/0264-9381/32/9/095009
LA English
DE critical collapse; exact solutions; AdS(3)
AB 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 not equal 0 these solutions reduce to the static Banados-Teitelboim-Zanelli (BTZ) family of vacuum solutions, with mass M = -alpha. For b not equal 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 sub-critical collapse, including the independence of the near-critical regime on the angle deficit of the spacetime. We analyze in the Lambda = 0 approximation the linear perturbations of the self-similar threshold solution, alpha = 0, and find that it has only one unstable growing mode, which qualifies it as a candidate critical solution for scalar field collapse.
ER