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 co de reproduces the critical phenomena (the Choptuik effect) in the clas sical limit and black-hole evaporation in the semiclassical limit. We then investigate the effect of evaporation on the critical behavior. T he introduction of the Planck length by the quantum theory suggests th at 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 intermed iate regime, evaporation is equivalent to a decrease of the initial am plitude. It does not change the echoing structure of the near-critical solutions. In the regime where black-hole masses are low and the quan tum effects are large, the semiclassical approximation breaks down and has no physical meaning. [S0556-2821(97)02018-3]. PACS number(s): 04. 25.Dm. 04.40.Dg, 04.60.Kz.