Scalar field collapse in three-dimensional AdS spacetime

Abstract

We describe results of a numerical calculation of circularly symmetric scalar field collapse in three spacetime dimensions with negative cosmological constant. The procedure uses a double null formulation of the Einstein-scalar equations. We see evidence of black hole formation on first implosion of a scalar pulse if the initial pulse amplitude $A$ is greater than a critical value $A_{\ast }$. Sufficiently near criticality the apparent horizon radius $r_{AH}$ grows with pulse amplitude according to the formula $r_{AH}\sim (A-A_{\ast }{)}^{0.81}$.

10 pages, 1 figure; references added, to appear in CQG(L)