  We offer a mathematically rigorous basis for the widely held suspicion that
full black hole evaporation is in tension with predictability. Based on
conditions expressing the global causal structure of evaporating black hole
spacetimes, we prove two theorems in Lorentzian geometry showing that such
spacetimes either fail to be causally simple or fail to be causally continuous.
These theorems, when combined with recent results \cite{AM} on the causal
structure of spacetimes with timelike boundary, bear significantly on the
question of whether these spacetimes permit for a predictable evolution.
