Short-Hair Black Holes and the Strong Cosmic Censorship Conjecture

Abstract: The singularity problem has always been a focus of physicists' research. In order to solve this problem, Penrose proposed the cosmic censorship conjecture, but verifying this conjecture in different situations still faces many challenges. In the context of short-hair black hole research, this paper explores whether the Strong Cosmic Censorship Conjecture (SCCC) is obeyed by the universe when it is disturbed by a scalar field. In this paper, we explore whether the short-hair black hole satisfies the SCCC under scalar field perturbations. Using the Weak Gravity Conjecture (WGC) and the WKB approximation method within the framework of general relativity, we systematically analyze the behavior of short-hair black holes under different parameter conditions. The focus is on whether violations of the SCCC occur when the black hole approaches extremal conditions. The results show that when the charge Q of the short-hair black hole approaches its extremal value, the SCCC is violated. However, as the order k of the black hole's metric equation and the angular momentum quantum number l increase, the phenomenon of SCCC violation is delayed. These findings indicate that the proximity of the black hole's charge Q to extremality, as well as the values of the angular momentum quantum number l and the order k, play crucial roles in exploring black hole physics and verifying the SCCC. This research not only reveals the behavior of short-hair black holes under extreme conditions but also provides a new perspective for further investigation of the SCCC.