The weak cosmic censorship conjecture (WCCC) of black holes is a fundamental hypothesis in general relativity. The proof of this hypothesis has become a frontier issue in the study of gravity. Recently, Sorce and Wald proposed a new version of the gedanken experiment and examined that the WCCC of Kerr-Newman (KN) black holes is valid under the second-order approximation of the matter fields perturbation. But it is not enough to study the WCCC under the second-order approximation because there is an additional condition that makes the validity of the hypothesis impossible to judge in this case. Therefore, the higher-order approximation of the perturbation process should be further considered to examine the conjecture strictly. Based on the new version of the gedanken experiment, from the two assumptions that the spacetime geometry satisfies the stability condition and that the matter fields should obey the null energy condition, we deduce the $n$th-order perturbation inequality and demonstrate that the event horizon of KN black holes always exists under the $n$th-order approximation of the matter fields perturbation. It indicates that the hypothesis is always satisfied under the arbitrary high-order approximation and also shows that the WCCC of KN black holes has been examined rigorously at the perturbation level.

中文翻译：

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高阶近似的格丹肯实验：克尔-纽曼黑洞不能被过度充电和过度旋转

黑洞的弱宇宙审查猜想（WCCC）是广义相对论的一个基本假设。这一假设的证明已成为引力研究的前沿问题。最近，Sorce 和 Wald 提出了新版本的 gedanken 实验，并检验了 Kerr-Newman (KN) 黑洞的 WCCC 在物质场扰动的二阶近似下是有效的。但是仅仅研究二阶近似下的WCCC是不够的，因为在这种情况下，还有一个额外的条件使得假设的有效性无法判断。因此，应进一步考虑摄动过程的高阶近似，以严格检验猜想。基于新版的格丹肯实验，$n$阶微扰不等式，并证明 KN 黑洞的事件视界总是存在于$n$物质场扰动的三阶近似。这表明该假设在任意高阶近似下总是得到满足，同时也表明 KN 黑洞的 WCCC 在微扰水平上得到了严格的检验。