Microscopic origin of black hole entropy and the Page curve

Determine the microscopic black hole degrees of freedom within gravitational, diffeomorphism-invariant field theories that account for both the Bekenstein–Hawking (Wald) entropy of black holes and the entanglement entropy required to reproduce the Page curve for evaporating black holes.

Background

The paper reviews recent progress showing that applying Ryu–Takayanagi-type prescriptions to evaporating black holes reproduces the Page curve, but emphasizes that these arguments do not identify the specific microscopic degrees of freedom responsible for the entropy and entanglement.

The authors frame this gap as an explicitly stated open question, connecting it to the longstanding issue of the microscopic origin of the Bekenstein–Hawking entropy. They then propose a resolution later in the paper using a generalized Ryu–Takayanagi formula that keeps contact with Hamiltonian phase space.