Globally hyperbolic evaporating black hole and the information loss issue

We discuss the information loss issue for completely evaporating black holes in the context of a globally hyperbolic spacetime that maintains unchanged the entire semiclassical picture except for the "last evaporation breath," which pertains to full quantum gravity. Even though observers outside the black hole cannot access information that enters the horizon, there is no actual loss of information imposed by the spacetime causal structure since it is carried over from one Cauchy surface to the next (provided the local evolution is unitary).