Causal connectability between quantum systems and the black hole interior in holographic duality

Abstract

In holographic duality an eternal AdS black hole is described by two copies of the boundary CFT in the thermal field double state. This identification has many puzzles, including the boundary descriptions of the event horizons, the interiors of the black hole, and the singularities. Compounding these mysteries is the fact that, while there is no interaction between the CFTs, observers from them can fall into the black hole and interact. We address these issues in this paper. In particular, (i) we reformulate the meeting-behind-the-horizon puzzle by introducing a concept called causal connectability for any two quantum systems (which can in principle interact with each other), and show that this simple bulk experiment cannot be described by the boundary system at finite \(N\); (ii) we present a resolution of the puzzle by arguing there are emergent type III\(_1\) von Neumann subalgebras in the operator algebra of the boundary system in the large \(N\) limit; (iii) the type III\(_1\) structure leads to an explicit construction in the boundary theory of the evolution operator for a bulk in-falling observer, making manifest the emergence of the black hole horizons, the interiors, and the associated causal structure.