Short-hair black holes and the strong cosmic censorship conjecture

Abstract

Abstract The singularity problem has always been a key focus of physicists’ research. To address this issue, Penrose proposed the cosmic censorship conjecture, with the Strong Cosmic Censorship Conjecture (SCCC) being particularly crucial. However, verifying SCCC in different scenarios still faces many challenges. This paper, set against the background of short-hair black holes, explores whether they obey SCCC when subjected to scalar field perturbations. Using the WKB method, Prony method, Lyapunov exponent, and Weak Gravity Conjecture (WGC), the behavior of a short-hair black hole under different parameter conditions was systematically analyzed. Numerical results indicate that as the charge $$ Q $$ Q of the short-hair black hole approaches its extremal value, the SCCC is violated. However, as the order $$ k $$ k of the metric equation and the angular quantum number $$ \ell $$ ℓ increase, the violation of SCCC is delayed. These results suggest that the proximity of the black hole’s charge $$ Q $$ Q to its extremal value, along with the size of the angular quantum number $$ \ell $$ ℓ and the order $$ k $$ k , play key roles in exploring the physical properties of black holes and verifying SCCC. Finally, research using the WGC shows that when the charge-to-mass ratio in a scalar field meets certain conditions, short-hair black holes can still comply with the SCCC under extreme conditions. This study not only reveals the behavior of short-hair black holes in extreme situations but also offers a new perspective for further exploration of such black holes.