Effects of quantum fields on singularity in spherical gravitational collapse

Using a semiclassical model for the formation and evaporation of a 4D black hole, we examine if the presence of a quantum matter source of the gravitational field can modify the occurrence of the classical singularity r = 0. In the limit r --> 0, we solve analytically the equations of the back-reaction for a massless scalar quantum field propagating in the space-time. We find two solutions and both are singular at r = 0.