Higher-Derivative Corrections to Entropy and the Weak Gravity Conjecture in Anti-de Sitter Space

Understand

We compute the four-derivative corrections to the geometry, extremality bound, and thermodynamic quantities of AdS-Reissner-Nordstr{\"o}m black holes for general dimensions and horizon geometries.

• We confirm the universal relationship between the extremality shift at fixed charge and the shift of the microcanonical entropy, and discuss the consequences of this relation for the Weak Gravity Conjecture in AdS.
• The thermodynamic corrections are calculated using two different methods: first by explicitly solving the higher-derivative equations of motion and second, by evaluating the higher-derivative Euclidean on-shell action on the leading-order solution.
• In both cases we find agreement, up to the addition of a Casimir energy in odd dimensions.