Choptuik Scaling and Quantum Effects in 2D Dilaton Gravity

We study numerically the collapse of massless scalar fields in two-dimensional dilaton gravity, both classically and semiclassically. At the classical level, we find that the black hole mass scales at threshold like $M_{\mathrm{b}\mathrm{h}}\propto \mathrm{\mid }p-p^{\ast }{\mathrm{\mid }}^{\gamma }$, where $\gamma \simeq 0.53$. At the semiclassical level, we find that in general $M_{\mathrm{b}\mathrm{h}}$ approaches a non-zero constant as $p\to p^{\ast }$. Thus, quantum effects produce a mass gap not present classically at the onset of black hole formation.