In the context of the conjectured AdS-CFT correspondence of string theory, we
consider a class of asymptotically Anti-de Sitter black holes whose conformal
boundary consists of a single connected component, identical to the conformal
boundary of Anti-de Sitter space. In a simplified model of the boundary theory,
we find that the boundary state to which the black hole corresponds is pure,
but this state involves correlations that produce thermal expectation values at
the usual Hawking temperature for suitably restricted classes of operators. The
energy of the state is finite and agrees in the semiclassical limit with the
black hole mass. We discuss the relationship between the black hole topology
and the correlations in the boundary state, and speculate on generalizations of
the results beyond the simplified model theory.Comment: 27 pages, LaTeX, using REVTeX v3.1 with amsfonts and epsf, with two
eps figures. (v3: references updated
