What is the name of the theoretical problem about whether information is destroyed inside evaporating black holes?

The theoretical problem about whether information is destroyed inside evaporating black holes is called the black hole information paradox.

Quantum mechanics says that a complete description of a physical system preserves information about its earlier state. Hawking’s calculation, published in 1974 and 1975, showed that black holes should emit thermal Hawking radiation. If a black hole eventually evaporates, that radiation appears not to retain enough information to reconstruct what fell in.

This creates a conflict between quantum theory and the semiclassical description of gravity. Proposed resolutions include information escaping through subtle correlations in the radiation, holographic descriptions, and black-hole complementarity. Physicists have not reduced the debate to one universally accepted explanation, but modern theoretical work strongly treats information preservation as a central requirement of quantum gravity.