Gedanken experiments at high-order approximation: Kerr black hole cannot be overspun

A bstract Sorce and Wald proposed a new version of gedanken experiments to examine the weak cosmic censorship conjecture (WCCC) in Kerr-Newmann black holes. However, their discussion only includes second-order approximation perturbation there exists an optimal condition such that validity WCCC is determined by higher-order approximations. Therefore, this paper, we extended discussions into high-order approximations study nearly extremal Kerr hole. After assuming spacetime satisfies stability matter fields satisfy null energy condition, based on Noether charge method Iyer Wald, completely calculate first four order inequalities discuss corresponding experiment overspin As result, find holes cannot be destroyed under fourth-order perturbation. Then, using mathematical induction, strictly prove n th inequality when ( − 1) are saturated. Using these results, 100 hole valid Our investigation implies might satisfied level.