Physical interpretation of the entropy mismatch

Clarify the physical interpretation of the discrepancy between de Sitter entropy and holographic entanglement entropy for general stationary braneworld spacetimes in higher-curvature gravity, including why a nonvanishing extrinsic-curvature contribution produces physically distinct entropy prescriptions and what fundamental distinction between the two entropies this difference represents.

Background

The paper establishes that de Sitter entropy and holographic entanglement entropy coincide for static asymptotically de Sitter braneworld spacetimes in Gauss–Bonnet and general Lovelock gravity, but generally differ for stationary spacetimes. The discrepancy is attributed to a contribution involving the extrinsic curvature of constant-time hypersurfaces, which vanishes in the static case and need not vanish in the stationary case.

Although the geometrical source of the mismatch is identified, the paper does not resolve its physical meaning. In particular, it leaves open why the extrinsic-curvature term should correspond to genuinely different entropy prescriptions and what conceptual distinction it reveals between gravitational horizon entropy and holographic entanglement entropy.