Simple Subsets of the Black Hole Interior*

Hawking radiation is notoriously difficult to decode. It has been often speculated that not just Hawking modes but more generally local operators anywhere inside a black hole have high computational complexity in the dual CFT. Using the characteristic initial value problem in the bulk, I will argue that some parts of the black hole interior are simple to decode: that is, there are local operators in the black hole interior that are simply reconstructible in the CFT; in fact, any local operator that lives between the event horizon and a certain type of outermost marginally trapped surface will be simple. Complex operators are constrained to the region behind the outermost marginally trapped (or extremal) surface, which I will argue by consistency of the holographic dictionary (not assuming cosmic censorship) must lie behind an event horizon.