Holographic Entanglement Entropy and Quantum Extremal Surfaces in Asymptotically Anti-de Sitter Spacetimes with Higher-Curvature Corrections

We present a theoretical study of holographic entanglement entropy, quantum extremal surfaces, and higher-curvature corrections (Lovelock/Gauss-Bonnet gravity) in asymptotically anti-de Sitter spacetimes within the framework of the AdS/CFT correspondence. Moving beyond standard Einstein gravity, we investigate Ryu-Takayanagi formulas and their generalized Engelhardt-Wall counterparts, variational equations for minimal area surfaces with conformal boundary conditions, and central charge scaling behaviors. Our analysis examines competing saddle points for sub-system entanglement, bulk metric reconstructions, and derives an original higher-order correction for holographic mutual information in the strong-coupling regime. Furthermore, we outline numerical metric reconstruction protocols for solving Einstein equations with higher-curvature terms.