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 nth 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.
Highlights
Proposed a new version of the gedanken experiments
We show the value of the parameter A2m of different integer m. These results show that the nearly extremal Kerr black hole cannot be overspun by the perturbation matter fields with the null energy condition under the higher-order approximation of perturbation
We extended the Sorce-Wald gedanken experiments into the higher-order approximations to study the weak cosmic censorship conjecture (WCCC) of a Kerr black hole under the perturbation process
Summary
We review the Noether charge and variational identity in Einstein gravity with the Lagrangian four-form. Considering an one-parameter family with the parameter λ, the kth-order variation of the field φ is defined by δkφ =. I.e., its kth derivative evaluated at λ = 0. Taking the derivative of the Lagrangian, we have dLgrav dλ. Are the on-shell equation of motion and the symplectic potential three-form separately. For any two-parameter family with parameters λ1 and λ2, we can define a symplectic current three form. The Noether current three-form Jζ associated with the vector field ζa is defined by. 1 (Cζ )abc = 8π eabcζdGde. It is necessary to note that the above identity holds for any spacetime configuration even if it does not satisfy the on-shell equation of motion Gab = 0
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