  We show how the traversable wormhole induced by a double-trace deformation of
the thermofield double state can be understood as a modular inclusion of the
algebras of exterior operators. The effect of this deformation is the creation
of a new region of spacetime deep in the bulk, corresponding to a non-trivial
center between the left and right algebras. This set-up provides a precise
framework for investigating how black hole interiors are encoded in the CFT. In
particular, we use modular theory to demonstrate that state dependence is an
inevitable feature of any attempt to represent operators behind the horizon.
Building on this geometrical structure, we propose that modular inclusions may
provide a more precise means of investigating the nascent relationship between
entanglement and geometry in the context of the emergent spacetime paradigm.
