Constraints on High-Order Gravitational Theories from Weak Cosmic Censorship

TL;DR

This paper investigates whether the weak cosmic censorship conjecture can constrain higher-order gravitational theories by testing black hole stability and deriving destruction conditions, thus providing a new way to evaluate the reasonableness of modified gravity models.

Contribution

It applies first-order Sorce-Wald gedanken experiments to higher-order gravity theories, establishing a criterion to test the validity of the weak cosmic censorship conjecture in these models.

Findings

Existence of a destruction condition for extremal black holes.

Constraints on quadratic and cubic gravitational theories derived from WCCC.

WCCC can serve as a tool to evaluate the reasonableness of modified gravity theories.

Abstract

Weak cosmic censorship conjecture (WCCC) is a basic principle that guarantees the predictability of spacetime and should be valid in any classical theories. One critical scientific question is whether the WCCC can serve as a constraint to the gravitational theories. To explore this question, we perform the first-order Sorce-Wald's gedanken experiments to test the WCCC in the higher-order gravitational theories and find that there exists a destruction condition $S_\text{ext}'(r_h)<0$ for the extremal black holes. To show the power of this condition, we evaluate the constraints given by WCCC in the quadratic and cubic gravitational theories. Our investigation makes an essential step toward applying WCCC to constrain the modified gravitational theories, and opens a new avenue to judge which theory is reasonable.