2-LOOP BACK-REACTION IN 2D DILATON GRAVITY

We calculate the two-loop quantum corrections, including the back-reac tion of the Hawking radiation, to the one-loop effective metric in a u nitary gauge quantization of the CGHS model of 2D dilaton gravity. The corresponding evaporating black hole solutions are analyzed, and cons istent semi-classical geometries appear in the weak-coupling region of the space-time when the width of the matter pulse is larger then the short-distance cutoff. A consistent semi-classical geometry also appea rs in the limit of a shock-wave matter. The Hawking radiation Aux rece ive's non-thermal corrections such that it vanishes for late times and the total radiated mass is finite. There are no static remnants for m atter pubes of finite width, although a BPP type static remnant appear s in the shock-wave limit. Semi-classical geometries without curvature singularities can be obtained as well, Our results indicate that high er-order loop corrections can remove the singularities encountered in the one-loop solutions.