Constraints on high-order gravitational theories from weak cosmic censorship

In this paper, we perform first-order Sorce-Wald's gedanken experiments to test the weak cosmic censorship conjecture (WCCC) in the higher-order gravitational theories. Based on the Noether charge method proposed by lyer and Wald and the null energy condition of the matter fields, we derive a first-order perturbation inequality. Using this result, we find that there exists a destruction condition S-ext' ,(r(h)) < 0 for the extremal black holes under the first-order approximation of perturbation. To show the power of this condition, we evaluate the constraints given by WCCC in the quadratic and cubic gravitational theories. Our investigation implies that besides the observation requirements such as the Solar System tests, the WCCC may also play some role in the selection of physically acceptable theories.