Weak Gravity Conjecture

The Weak Gravity Conjecture, proposed by Arkani-Hamed, Motl, Nicolis, and Vafa in 2006, asserts that quantum-gravity theories contain sufficiently charged objects, schematically requiring a charge-to-mass ratio at least that of an extremal black hole. Its precise formulation, especially in anti-de Sitter space, remains unsettled.

Known results

• The original proposal did not prove extremal black-hole decay or the bound (Arkani-Hamed, Motl, Nicolis, and Vafa, 2006).
• Higher-derivative and entropy arguments support the conjecture in broad classes but require additional assumptions (Cheung, Liu, and Remmen; Cheung et al., 2018).
• Explicit compactification examples contradict lattice and other stronger versions, without refuting every mild version.
• Numerical anti-de Sitter studies support a connection with cosmic censorship but provide no general proof (Crisford and Santos, 2017).

2026 near-horizon bounds

Saeed Noori Gashti, Behnam Pourhassan, and İzzet Sakallı derive model-dependent bounds relating the conjecture to near-horizon $\mathrm{AdS}_2$ data, including dRGT massive gravity and Einstein–ModMax black holes. The reported symbolic and numerical checks support the calculation within those assumptions, but do not establish the conjecture for arbitrary quantum-gravity theories; independent assessment was not found.

Current status (as of October 2026): Model-dependent near-horizon bounds have been claimed, but the general Weak Gravity Conjecture remains open and the new derivation is unverified.