Single-exterior black holes and the AdS-CFT conjecture

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.