Relating black holes in two and three dimensions

The three-dimensional black hole solutions of Bañados, Teitelboim, and Zanelli (BTZ) are dimensionally reduced in various different ways. Solutions are obtained to the Jackiw-Teitelboim theory of two-dimensional gravity for spinless BTZ black holes, and to a simple extension with a nonzero dilaton potential for black holes of fixed spin. Similar reductions are given for charged black holes. The resulting two-dimensional solutions are themselves black holes, and are appropriate for investigating exact "$S$-wave" scattering in the BTZ metrics. Using a different dimensional reduction to the string-inspired model of two-dimensional gravity, the BTZ solutions are related to the familiar two-dimensional black hole and the linear dilaton vacuum.