Testing The Weak Cosmic Censorship Conjecture in Short Haired Black Holes

The Weak Cosmic Censorship Conjecture is a hypothesis regarding the properties of event horizons and singularities during the formation of black holes, stating that singularities are always encompassed by the event horizons(TEH) of black holes, thus preventing naked singularities from affecting the causal structure of spacetime. In this paper, we explore the Weak Cosmic Censorship Conjecture in the context of rotating hairy black holes, aiming to understand the impact of hairiness on the conjecture for Kerr black holes. We investigate whether TEH of rotating hairy black holes can be disrupted by incoming test particles and scalar fields. When test particles and scalar fields incident on the rotating hairy black hole are found. In extreme cases, when considering a second order approximation, if the parameter $\kappa$ (The parameter here is a function related to hair strength $\kappa(Q_m^{2k})$.)falls within the range of $0<\kappa<\sqrt{1/3}$, TEH of a hairy black hole can be disrupted. Conversely, in the range of $\sqrt{1/3}<\kappa<1$, TEH of a hairy black hole cannot be disrupted. When considering the second order approximation in near extreme cases, the parameter $\kappa$, within the range of $0<\kappa<1$, can lead to the disruption of TEH in this spacetime. When an incident scalar field is present, in near extreme conditions, TEH of a rotating short hair black hole cannot be disrupted. Therefore, the value of the parameter $\kappa$ reveals the connection between rotating short hair black holes and the weak cosmic censorship conjecture, indicating that the presence of short hair significantly affects TEH of black holes. This will aid in further understanding the nature of rotating short hair black holes.