Semiclassical extremal black holes

Extremal black holes are studied in a two-dimensional model motivated by a dimensional reduction from four dimensions. Their quantum-corrected geometry is calculated semiclassically and a mild singularity is shown to appear at the horizon. Extensions of the geometry past the horizon are not unique but there are continuations free from malevolent singularities. A few comments are made about the relevance of these results to four dimensions and to the study of black hole entropy and information loss.