Black hole evaporation and quantum gravity in two dimensions

We begin by introducing the puzzles associated with the complete evaporation of black holes, and various proposals for their resolution. We focus briefly on some generalities of covariant field theories of one scalar field coupled to gravity in two dimensions. From here we go on to study in greater detail a particular model of this type coupled to massless matter fields, with black hole solutions, and study a proposal for calculating the evaporation of this two-dimensional black hole. We point out the flaws and successes of the general proposal. This leads us to study in greater detail the possibility of a consistent scenario in which the final state of the evaporation is a remnant state that can consume arbitrarily large amounts of information. We propose to study Hawking evaporation in a wider class of nonsingular models having black hole solutions. Finally we make some general comments on the significance of these calculations in two dimensions to the fundamental problem of understanding the end-point of Hawking evaporation in four dimensions.