One-Loop Effective Action for Spherical Scalar Field Collapse

We calculate the complete one-loop effective action for a spherical scalar field collapse in the large radius approximation. This action gives the complete trace anomaly, which beside the matter loop contributions, receives a contribution from the graviton loops. Our result opens a possibility for a systematic study of the back-reaction effects for a real black hole.Comment: 14 pages, slightly expanded version to appear in Class. Quant. Gra