Single-exterior black holes and the AdS-CFT conjecture

TL;DR

The paper investigates single-exterior AdS_3 black holes within the AdS/CFT framework by constructing a simplified boundary CFT model that maps bulk RP^2 geon spacetimes to pure boundary states. It shows that, although the boundary state is pure, correlations between left- and right-moving sectors induce thermal expectation values for observables on a single boundary, with the energy reproducing the bulk mass in the semiclassical large-horizon limit. The analysis explicitly computes the BTZ and RP^2 geon boundary states, including oscillator and zero-mode sectors, and demonstrates consistency with Hawking temperature and bulk mass, while highlighting subtleties arising from zero modes and non-normalizable ground states. The work also extends the discussion to internal dimensions and a Swedish geon, outlining how bulk topology imprints on boundary quantum states and outlining future steps toward embedding these results in the full Maldacena-CFT framework.

Abstract

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.