Destroying extremal Kerr-Newman black holes with test particles

It has been shown that a nearly extremal black hole can be overcharged or overspun by a test particle if radiative and self-force effects are neglected, indicating that the cosmic censorship might fail. In contrast, the existing evidence in literature suggests that an extremal black hole cannot be overcharged or overspun in a similar process. In this paper, we show explicitly that even an exactly extremal black hole can be destroyed by a test particle, leading to a possible violation of the cosmic censorship. By considering higher-order terms, which were neglected in previous analysis, we show that the violation is generic for any extremal Kerr-Newman black hole with nonvanishing charge and angular momentum. We also find that the allowed parameter range for the particle is very narrow, indicating that radiative and self-force effects should be considered and may prevent violation of the cosmic censorship.