Constraints on Low-Energy Effective Theories from Weak Cosmic Censorship

We examine the weak cosmic censorship conjecture (WCCC) for the extremal charged black hole in possible generalizations of Einstein-Maxwell theory due to the high-order corrections, up to fourth-derivative terms. Our derivation is based on Wald's gedanken experiment to destroy an extremal black hole. We find that the WCCC no longer holds for all possible generalizations. Thus, the WCCC can serve as a new constraint to the high-order effective field theories. However, our constraint is independent of photon's self-interactions so that precision measurement of quantum electrodynamics cannot constrain the WCCC. For higher-dimension operators induced by the one-loop correction for the minimally coupled spinor and scalar to gravity, our constraint is satisfied.