Phase transition for gravitationally collapsing dust shells in 2+1 dimensions

The collapse of thin dust shells in (2+1)-dimensional gravity with and without a cosmological constant is analyzed. A critical value of the shell’s mass as a function of its radius and position is derived. For ΛM∼${\mathit{c}}_{\mathit{p}}$(p-${\mathit{p}}^{\mathrm{*}}$ ${)}^{\mathrm{\beta }}$, where β=1/2 and M is a naturally defined order parameter. We find no phase transition in crossing from an open to closed space. The critical exponent appears to be universal for spherically symmetric dust. The critical solutions are analogous to higher dimensional extremal black holes. All four phases coexist at one point in solution space corresponding to the static extremal solution.