MODULI-SPACE OF ASYMPTOTICALLY ANTI-DESITTER SPACE-TIMES IN 2+1-DIMENSIONS

Setting an ansatz that the metric is expressible by a power series of the inverse radius and taking a particular gauge choice, we construct a ''general solution'' of (2 + 1)-dimensional Einstein equations with a negative cosmological constant in the case where the space-time is asymptotically anti-de-Sitter Our general solution turns out to be parametrized by two centrally extended quadratic differentials on S-1. In order to include three-dimensional black holes naturally in our general solution, it is necessary to exclude the region inside the horizon. We also discuss the relation of our general solution to the moduli space of hat SL(2, R) x SL(2, R) connections.