Weak cosmic censorship with self-interacting scalar and bound on charge to mass ratio

We study the model of Einstein-Maxwell theory minimally coupling to a massive charged self-interacting scalar field, parameterized by quartic and hexic coupling, labelled $\lambda$ $\beta$, respectively. In absence there is class counterexamples cosmic censorship. Moveover, we investigate properties full nonlinear solution with nonzero argue that, assuming field sufficiently large charge above one certain bound, these can be removed. particular, this bound on for no longer equal weak gravity free case. case, bounds are below case $\lambda<0$, while $\lambda>0$. Meanwhile, in both $\beta>0$ $\beta<0$.