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

TL;DR

This paper extends the analysis of gedanken experiments testing the weak cosmic censorship conjecture in Kerr black holes to high-order perturbations, concluding that such black holes cannot be overspun and thus support the conjecture.

Contribution

It provides a rigorous proof that Kerr black holes cannot be overspun under perturbations up to the 100th order, strengthening the validity of the weak cosmic censorship conjecture.

Findings

Kerr black holes cannot be overspun under fourth-order perturbation.

Higher-order perturbation inequalities are satisfied, supporting WCCC.

The WCCC remains valid under perturbations up to the 100th order.

Abstract

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