Remarks on harmonic maps, solitons, and dilaton gravity

Abstract

Another connection of harmonic maps to gravity is presented. Using 1-soliton and anti-soliton solutions of the sine-Gordon equation, we construct a pair of harmonic maps that we express in terms of a particular dilaton field in Jackiw-Teitelboim gravity. This field satisfies a linearized sine-Gordon equation. We use it also to construct an explicit transformation that relates the corresponding solitonic metric to a two dimensional black hole metric.