"Moduli Space" of Asymptotically Anti-de Sitter Spacetimes in (2+1)-Dimensions

Details "Moduli Space" of Asymptotically Anti-de Sitter Spacetimes in (2+1)-Dimensions "Moduli Space" of Asymptotically Anti-de Sitter Spacetimes in (2+1)-Dimensions

1994-11-23

arxiv.org/abs/hep-th/9411166v1

Int.J.Mod.Phys.A10:4139-4160,1995

Physics

High Energy Physics

High Energy Physics - Theory

23 pages, Latex

Scientific paper

10.1142/S0217751X95001911

Setting an ansats 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's equations with a negative cosmological constant in the case where the spacetime 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 3-dimensional Black Holes naturally into 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 flat $\tilde{SL}(2,R)\times\tilde{SL}(2,R)$ connections.

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