Is information lost in black holes?

The black-hole information problem asks whether an initially quantum state can evolve into featureless thermal radiation that no longer retains its distinctions. Horizon entropy and the growth of area account for a thermodynamic budget; they do not alone provide a reversible map from infalling states to outgoing radiation. OPH approaches the problem through observer records, restricted access and the information associated with region boundaries. It must distinguish a record becoming inaccessible to an outside observer from its destruction in the complete process. A complete solution needs a compatible quantum evolution, an evaporating geometry and recoverable correlations in the radiation. The boundary bookkeeping supplies a proposed route, while a physical evaporation construction must establish the decisive transfer. A horizon diagram by itself does not settle it.

See also What happens inside a black hole?, What replaces the singularities in the Big Bang and black holes?

Sources: Observer spacetime and the conditional Einstein reconstruction

Also in Prologue: No Source Code, No Documentation.