Multi-black-hole sectors of ${\mathrm{AdS}}_3$ gravity

We construct and discuss solutions of $\mathrm{SO}(1,2)\mathrm{}\times \mathrm{SO}(1,2)\mathrm{}$ Chern-Simons theory which correspond to multiple BTZ black holes. These solutions typically have additional singularities, the simplest cases being special conical singularities with a $2\pi$ surplus angle. There are solutions with singularities inside a common outer horizon, and other solutions with naked conical singularities. Previously such singularities have been ruled out on physical grounds, because they do not obey the geodesic equation. We find however that the Chern-Simons gauge symmetry may be used to locate all such singularities to the horizons, where they necessarily follow geodesics. We are therefore led to conclude that these singular solutions correspond to physically sensible geometries. Boundary charges at infinity are only sensitive to the total mass and spin of the black holes, and not to the distribution among the black holes. We therefore argue that a holographic description in terms of a boundary conformal field theory should represent both single and multiple BTZ solutions with the same asymptotic charges. Then sectors with multiple black holes would contribute to the black hole entropy calculated from a boundary CFT.