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Since the Weak Cosmic Censorship Conjecture was proposed, research on thisconjecture has been ongoing. This paper explores the conjecture in black holesthat are closer to those existing in the real universe (i.e., rotating blackholes enveloped by dark matter). In this paper, we obtained a first-ordercorrected analytical solution for the black hole event horizon through anapproximate solution. The validity of the first-order corrected analyticalsolution will be provided in the appendix. We conduct our study by introducinga test particle and a scalar field into the black hole. Our conclusions showthat, in extremal case, both a test particle and a scalar field can disrupt theevent horizon of the Kerr-like black hole; in near-extremal case, both a testparticle and a scalar field can disrupt the event horizon of the Kerr-likeblack hole. When cold dark matter is not considered, the conclusion isconsistent with previous research.

Destroying the Event Horizon of Cold Dark Matter-Black Hole System