Testing the Weak Cosmic Censorship Conjecture via Test Particle–Induced Overcharging/Overspinning of Kerr–Newman–Modified Gravity Black Hole

We examine the weak cosmic censorship conjecture (WCCC) violation by throwing a charged and rotating test particle into a Kerr–Newman–modified gravity black hole (KN–MOG BH). The result depends on several factors, such as the relative sign of the particle’s charge and its direction of rotation with respect to black hole (BH). Additionally, the interplay between the MOG parameter, the BH’s angular momentum, and its charge plays a significant role. Taking all these into account, we determine the lower and upper bounds of the particle’s energy, angular momentum, and charge for which the event horizon disappears. We find a narrow gap between the lower and upper bounds of the particle’s parameters for both extremal and nonextremal BHs. It is observed that, as the MOG parameter increases, the gap between these bounds widens. Our analysis shows that the WCCC can be violated in both extremal and nonextremal KN–MOG BHs, provided the particle’s parameters are precisely adjusted. Earlier investigations analyzed this scenario without incorporating the MOG parameter α . Our analysis reveals that incorporating α significantly expands the WCCC violation ranges of particle parameters in both extremal and nonextremal KN–MOG BHs. By applying the hoop conjecture (HC), we find that the WCCC is upheld for a general KN–MOG BH when a sufficiently large number of particles are absorbed.