Analytical treatment of critical collapse in 2+1 dimensional AdS spacetime: a toy model

Abstract

We present an exact collapsing solution to 2+1 gravity with a negative cosmological constant minimally coupled to a massless scalar field, which exhibits physical properties making it a candidate critical solution. We discuss its global causal structure and its symmetries in relation with those of the corresponding continously self-similar solution derived in the $\Lambda=0$ case. Linear perturbations on this background lead to approximate black hole solutions. The critical exponent is found to be $\gamma = 2/5$.Comment: 22 pages, 6 figures. Major changes in the discussions of Sects. 2 and 5. The value of the critical exponent has been revised to \gamma = 2/