Extending the weak cosmic censorship conjecture to the charged Buchdahl star by employing the gedanken experiments

Abstract: In this paper, we wish to investigate the weak cosmic censorship conjecture (WCCC) for the non black hole object, Buchdahl star and test its validity. It turns out that the extremal limit for the star is over-extremal for black hole, $Q^2/M^2 \leq 9/8 >1$; i.e., it could have $9/8 \geq Q^2/M^2 > 1$. By carrying out both linear and non-linear perturbations, we establish the same result for the Buchdahl star as well. That is, as for black hole it could be overcharged at the linear perturbation while the result is overturned when the non-linear perturbations are included. Thus WCCC is always obeyed by the Buchdahl star.