Overcharging Extremal Rotating Black Holes

TL;DR

This work addresses whether the weak cosmic censorship conjecture can constrain modified gravity theories by testing if extremal rotating black holes can be overcharged via test-body absorption. It introduces a theory-agnostic rotating black hole metric with a horizon function and extremality conditions, and derives simultaneous entering and overcharging inequalities to identify viable parameter regions. Applying the framework to a leading-order deviation parameter $\alpha_3$ in a slowly rotating, Einstein–Æther–like spacetime, the authors show that $\alpha_3<0$ preserves WCC while $\alpha_3>0$ can permit overcharging, thus constraining the sign of deviations from Kerr–Newman. The results offer a principled, physics-based method to bound beyond-GR models, while highlighting the importance of incorporating backreaction and exploring non-axisymmetric cases in future work.

Abstract

In this work, we use the weak cosmic censorship conjecture(WCC) to constrain black hole solutions in modified gravity theories. While Wald showed that extremal Kerr-Newman black holes in general relativity cannot be overcharged by test charged particles, this protection may fail in theories beyond general relativity. We have considered generic rotating black hole solutions beyond the Kerr-Newman family and examined particle absorption processes that could lead to overcharging and the emergence of naked singularities. Identifying regions of parameter space where WCC is violated allows us to place direct, physically motivated bounds on deviations from general relativity.