Multi-black-hole geometries in (2+1)-dimensional gravity

Generalizations of the black hole geometry of Bañados, Teitelboim, and Zanelli (BTZ) are presented. The theory is three-dimensional vacuum Einstein theory with a negative cosmological constant. The $n$-black-hole solution has $n$ asymptotically anti-de Sitter "exterior" regions that join in one "interior" region. The geometry of each exterior region is identical to that of a BTZ geometry; in particular, each contains a black hole horizon that surrounds (as judged from that exterior) all the other horizons. The interior region acts as a closed universe containing $n$ black holes. The initial state and its time development are discussed in some detail for the simple case when the angular momentum parameters of all the black holes vanish. A procedure to construct $n$ black holes with angular momentum (for $n>~4$) is also given.