On the (In)equivalence of de Sitter and Holographic Entanglement Entropies in Lovelock Gravity

Abstract: We investigate the relation between de Sitter entropy and holographic entanglement entropy in higher-curvature gravity and its braneworld realization. Using the canonical formulation of the gravitational action and the Euclidean gravitational path integral, we derive the de Sitter entropy, including contributions from higher-curvature surface terms, and compare it with the holographic entanglement entropy obtained from the corresponding entropy functional. We first consider Gauss-Bonnet gravity and show that the two entropies coincide for static asymptotically de Sitter braneworld spacetimes on the RS II model, while they generally differ for stationary spacetimes. The mismatch in the stationary case arises from an extrinsic-curvature contribution associated with the constant-time surface, which vanishes for static configurations but is generally nonzero for stationary geometries. We then extend the analysis to general Lovelock gravity and show that the agreement between the de Sitter entropy and holographic entanglement entropy persists for static asymptotically de Sitter braneworld spacetimes in the RS II model beyond the Gauss-Bonnet case. We also comment that the same distinction between static and stationary configurations applies to braneworld black holes: the black hole entropy agrees with the holographic entanglement entropy in the static case, while the two generally differ for stationary braneworld black holes. Our results clarify the relation between gravitational and holographic entropies in higher-curvature gravity and provide a broader perspective on holographic correspondence in Lovelock theories and their braneworld realizations.