Spherical collapse of a massless scalar field with semiclassical corrections

We investigate numerically, spherically symmetric collapse of a scalar field in the semiclassical approximation. We first verify that our code reproduces the critical phenomena (the Choptuik effect) in the classical limit and black-hole evaporation in the semiclassical limit. We then investigate the effect of evaporation on the critical behavior. The introduction of the Planck length by the quantum theory suggests that the classical critical phenomena, which are based on a self-similar structure, will disappear. Our results show that when quantum effects are not strong enough, critical behavior is observed. In the intermediate regime, evaporation is equivalent to a decrease of the initial amplitude. It does not change the echoing structure of the near-critical solutions. In the regime where black-hole masses are low and the quantum effects are large, the semiclassical approximation breaks down and has no physical meaning.