Establishing a complete quantum gravity description that defines S_BH as a von Neumann entropy

Establish a complete quantum gravity framework in which the black hole entropy S_BH appearing in the island formula is a well-defined von Neumann entropy, providing a precise operational meaning for S_BH within a full quantum gravity description of evaporating black holes.

Background

In formulating the island prescription, the paper distinguishes between semiclassical entropies computed for quantum fields on subregions and the fine-grained black hole entropy S_BH, which is intended to be the von Neumann entropy in a complete quantum gravity description. While semiclassical ingredients are well-defined, a fully specified quantum gravity framework that rigorously defines S_BH is not yet available.

Clarifying and formalizing S_BH within a complete quantum gravity description would ground the island formula on a firm microscopic footing and remove an important conceptual gap in current treatments of the Page curve.