Lodged in the throat: Internal infinities and AdS/CFT

In the context of AdS₃/CFT₂, we address spacetimes with a certain sort of internal infinity as typified by the extreme BTZ black hole. The internal infinity is a null circle lying at the end of the black hole's infinite throat. We argue that such spacetimes may be described by a product CFT of the form CFT_L⊗CFT_R, where CFT _R is associated with the asymptotically AdS boundary while CFT _L is associated with the null circle. Our particular calculations analyze the CFT dual of the extreme BTZ black hole in a linear toy model of AdS₃/CFT₂. Since the BTZ black hole is a quotient of AdS₃, the dual CFT state is a corresponding quotient of the CFT vacuum state. This state turns out to live in the aforementioned product CFT. We discuss this result in the context of general issues of AdS/CFT duality and entanglement entropy.