# Weak gravity conjecture For various reasons, quantum gravity physicists believe that gravity should be the weakest force of all. ## Refs - reviews and lectures - [[HarlowHeidenreichReeceRudelius2022]][](https://arxiv.org/pdf/2201.08380.pdf) ## Definitions - **mild form**: quantum or higher derivative corrections should decrease the mass of large extremal charged black holes at fixed charge - **BH version**: it should be possible for an extremal black hole to emit a smaller black hole ## Aspects - [[McInnes2021]][](https://arxiv.org/pdf/2104.07373.pdf): for AdS${}_4$-Kerr-Newman BHs to emit a smaller BH, the emiited BH must be rather exotic, having an angular horizon - [[McInnes2022]][](https://arxiv.org/pdf/2201.01939.pdf): planar BHs may bifurcate without decreasing the entropy (so not violating [[0005 Black hole second law]]) - [[SadeghiShokriAlipourGashti2022]][](https://arxiv.org/pdf/2203.03378.pdf) - hyperscaling violating BH and Kerr-Newman - [[2023#Kehagias, Kokkotas, Riotto, Taskas, Tringas]] - looking for and finding overcharged objects (in [[0554 Einstein gravity|General Relativity]]) ## Relation to [[0006 Higher-derivative gravity|HDG]] - [[NoumiSatake2022]][](https://arxiv.org/pdf/2210.02894.pdf): higher derivative corrections decrease tension-to-charge ratios of extremal black branes as implied by the weak gravity conjecture, if four-derivative couplings follow scattering positivity bounds - [[2018#Cheung, Liu, Remmen]]: black hole entropy considerations ## Derivation - from Euclidean gravity: [[2021#Harlow, Ooguri]] ## Flat v.s. AdS From [[HorowitzSantos2019]][](https://arxiv.org/abs/1901.11096): > The weak gravity conjecture in AdS differs from the asymptotically flat version. To derive the new bound, we require that extremal charged black holes can decay. In flat space, this is a purely quantum mechanical instability, but in AdS it turns out to give rise to a classical instability. This instability is the so called charged superradiant instability [11, 12] whose endpoint has been studied over the past decade [13–19]. ## Related - [[0182 Lattice WGC]]