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

TL;DR

This paper explores how black hole interiors and horizons emerge in holographic duality, introducing the concept of causal connectability to determine when two quantum systems can develop a shared horizon structure.

Contribution

It provides a boundary formulation for in-falling observers, shows the emergence of horizons in the infinite N limit, and introduces causal connectability as a criterion for emergent horizon structures.

Findings

Boundary formulation of in-falling observers

Sharp horizons emerge only at infinite N

Causal connectability as a criterion for horizon emergence

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, we (i) present a boundary formulation of a class of in-falling bulk observers; (ii) present an argument that a sharp bulk event horizon can only emerge in the infinite $N$ limit of the boundary theory; (iii) give an explicit construction in the boundary theory of an evolution operator for a bulk in-falling observer, making manifest the boundary emergence of the black hole horizons, the interiors, and the associated causal structure. A by-product is a concept called causal connectability, which is a criterion for any two quantum systems (which do not need to have a known gravity dual) to have an emergent sharp horizon structure.