Critical scalar field collapse in AdS_3: an analytic approach

Abstract: We present an analytical solution of a massless scalar field collapsing in a three dimensional space-time with a negative cosmological constant, i.e. asymptotically AdS_3. The Einstein and scalar field equations are formulated using double null Poincare coordinates. Trapping horizons form when a critical parameter is p > 1. There are indications that the horizon radius r_AH scales like r_AH ~ (p-1)^1/4 and the black hole mass as M ~ r_AH^2 ~ (p-1)^1/2, i.e. with a critical mass exponent of 1/2.