Quantum gravity effects in the CGHS model of collapse to a black hole

Abstract

We show that only a sector of the classical solution space of the CGHS model describes the formation of black holes through the collapse of matter. This sector has either right or left moving matter. We describe the sector which has left moving matter in canonical language. In the nonperturbative quantum theory all operators are expressed in terms of the matter field operator which is represented on a Fock space. We discuss the existence of large quantum fluctuations of the metric operator when the matter field is approximately classical. We end with some comments which may pertain to Hawking radiation in the context of the model.