No abstract

It was argued in the letter recently by B. Chen et. al [Phys. Rev. Lett. 126, 031102 (2021)] that the weak cosmic censorship conjecture (WCCC) can serve as a new constraint to the higher-order effective field theories. In their letter, they performed the Sorce-Wald's gedanken experiment to destroy an extremal black hole under the first-order approximation. However, after examining the calculation in their latter, we find that a key error occurs in their black hole solution. We recalculate their black hole solution and perform it to reexamine the WCCC. As a result, we find that after correcting the solution, the extremal black hole in the high-order theory they focus on cannot be destroyed under the first-order approximation of perturbation based on Sorce-Wald's gedanken experiment. This result is contrary to the one in their letter where there are some destructions of the extremal black hole. Moreover, we also generalize their discussion to a more general theory with Lagrangian L (g ab , R abcd , F ab ) and show that the extremal black hole cannot be destroyed under the first-order approximation when S ′ (r h ) > 0 with S(r h ) the black hole entropy; but it can be destroyed if S ′ (r h ) < 0 and therefore the WCCC is violated in these situations. Our results indicate that the Einstein-Maxwell gravity with some small corrections will obey the WCCC since S ′ (r h ) > 0 in these cases. However, when we consider some finite modification of the gravity, such as Lovelock gravity, there will exist some violations of WCCC. Therefore, our results also imply that the WCCC can play a natural role to constrain the modified gravitational theories.

After considering the quantum corrections of Einstein-Maxwell theory, the effective theory will contain some higher-curvature terms and nonminimally coupled electromagnetic fields. In this paper, we study the first law of black holes in the gravitational electromagnetic system with the Lagrangian ℒ(gab, Rabcd, Fab). Firstly, we calculate the Noether charge and the variational identity in this theory, and then generically derive the first law of thermodynamics for an asymptotically flat stationary-axisymmetric symmetric black hole without the requirement that the electromagnetic field is smooth on the bifurcation surface. Our results indicate that the first law of black hole thermodynamics might be valid for the Einstein-Maxwell theory with some quantum corrections in the effective region.

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.