Weak cosmic censorship with excited scalar fields and bound on charge-to-mass ratio

Recent study in [1] discovered that introducing a massive charged scalar field and requiring the Weak Gravity Conjecture (WGC) to hold can eliminate a class of Weak Cosmic Censorship Conjecture (WCCC) counterexamples in anti-de Sitter spacetime, indicating a potential connection between WCCC and WGC. In this paper, we extend the study to the case of excited-state scalar fields, and numerically construct the static solutions of excited massive charged scalar fields coupled to the Einstein-Maxwell field in four dimensional spacetime with asymptotically anti-de Sitter boundary conditions. In the absence of scalar field, there is a class of counterexamples to cosmic censorship. However, after adding the scalar field with sufficiently large charge, the original counterexamples can be removed and cosmic censorship is preserved. We find this conclusion also applies to the excited-state of scalar field. There is a minimum value $q_c^{\text{bound}}$ \( {q}_c^{\textrm{bound}} \) . When the charge of the excited scalar field is larger than this minimum value, for sufficiently large boundary electric amplitude a, there will not appear a region with arbitrarily large curvature. That means there exists lower bound on the charge for excited state fields which protects cosmic censorship from being violated.