Comment on "Constraints on Low-Energy Effective Theories from Weak Cosmic Censorship"

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.

Constraints on High-Order Gravitational Theories from Weak Cosmic Censorship

“…However, in Ref. [11], we found there exists an error in their letter. After correcting it, their discussion cannot give the constraint to the gravitational theory.…”

“…However, in Ref. [11], we reexamined their letter and found that key errors occur. After correcting the errors, their discussion cannot give the constraint to the high-order theories.…”