Higher-derivative corrections to entropy and the weak gravity conjecture in Anti-de Sitter space

Abstract

We compute the four-derivative corrections to the geometry, extremality bound, and thermodynamic quantities of AdS-Reissner-Nordström 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. We derive the bounds on the four-derivative Wilson coefficients implied by the conjectured positivity of the leading corrections to the microcanonical entropy of thermodynamically stable black holes. These include the requirement that the coefficient of Riemann-squared is positive, meaning that the positivity of the entropy shift is related to the condition that c − a is positive in the dual CFT. We discuss implications for the deviation of η/s from its universal value and a potential lower bound.

Higher-derivative supergravity, AdS4 holography, and black holes

“…Indeed, even though it evaluates to zero on-shell for all explicit solutions we have studied, its variation with respect to the metric is non-zero, which allows us to cancel bulk terms in the variation of S W 2 and end up with a welldefined boundary stress-tensor. The presence of this novel boundary term also explains the discrepancy between our results and those of [71], where it was argued that certain bulk four-derivative terms cannot affect the mass of the black hole. Our results therefore serve as an important reminder of the significance of finite boundary counterterms in holographic settings.…”

“…Another proposed version of the WGC for black holes posits that the same combination of higher-derivative operators control corrections to the charge-to-mass ratio as well as the entropy of the black hole. This has been demonstrated explicitly in a number of different examples [71,[78][79][80], all of which take the schematic form…”

“…This opens up a scenario where charged black holes can decay into smaller charged black holes, thus avoiding the remnant problem in a universal way that makes no reference to the field content of the theory beyond gravity and the U(1) gauge field. It has been argued in a number of bottom-up approaches that this black hole version of the WGC will hold if certain assumptions are placed on the UV-completion of the theory, including positivity of black hole entropy corrections [71,[78][79][80], unitarity and causality [81][82][83], and scattering amplitude positivity [84,85]. Most of these analyses are for asymptotically flat black holes, therefore it is worthwhile to further our understanding of the black hole WGC in asymptotically-AdS spacetimes.…”

“…the mass shift at fixed charge is negative) will correspond to positive entropy corrections. This has led to a new version of the black hole WGC in [71,78,79] that posits that the entropy corrections due to higher-derivative effects in a UV-complete theory of gravity must be positive:…”

D = 5 rotating black holes in Einstein-Gauss-Bonnet gravity: mass and angular momentum in extremality

“…It was recently shown [5] that the mass change of the extremal Reissner-Nordström (RN) black hole under the higher order correction is opposite in sign to the change of entropy, therefore providing a strong JHEP01(2021)201 evidence of the Weak Gravity Conjecture (WGC) [6]. Many interesting works follow, e.g., [7][8][9][10][11][12][13].…”