Nonsingular Lagrangians for Two Dimensional Black Holes

We introduce a large class of modifications of the standard lagrangian for two dimensional dilaton gravity, whose general solutions are nonsingular black holes. A subclass of these lagrangians have extremal solutions which are nonsingular analogues of the extremal Reissner-Nordstrom spacetime. It is possible that quantum deformations of these extremal solutions are the endpoint of Hawking evaporation when the models are coupled to matter, and that the resulting evolution may be studied entirely within the framework of the semiclassical approximation. Numerical work to verify this conjecture is in progress. We point out however that the solutions with non-negative mass always contain Cauchy horizons, and may be sensitive to small perturbations.