  There is a possibility that the event horizon of a Kerr-like black hole with
perfect fluid dark matter (DM) can be destroyed, providing a potential
opportunity for understanding the weak cosmic censorship conjecture of black
holes. In this study, we analyze the influence of the strength parameter of
perfect fluid DM on the destruction of the event horizon of a Kerr-like black
hole with spinning after injecting a test particle and a scalar field. We find
that, when a test particle is incident on the black hole, the event horizon is
destroyed by perfect fluid dark matter for extremal black holes. For nearly
extremal black holes, when the dark matter parameter satisfies $\alpha \in
\left (-r_{h} , 0\right ) \cup \left ( r_{h} ,k_2\right )$ i.e.$(A<0)$, the
event horizon of the black hole will not be destroyed; when the dark matter
parameter satisfies $\alpha \in\left ( k_1 ,-r_{h} \right ]\cup
\left[0,r_{h}\right ]$ i.e.$(A\ge 0)$, the event horizon of the black hole will
be destroyed. When a classical scalar field is incident into the black hole in
the extremal black hole case, we find that the range of mode patterns of the
scalar field that can disrupt the black hole event horizon is different for
different values of the perfect fluid dark matter strength parameter. In the
nearly extremal black hole case, through our analysis, we have found when
$\alpha\neq0 $ and $\alpha\neq\pm\ r_h$ i.e.$A\neq0$, the event horizon of the
black hole can be disrupted. Our research results indicate that dark matter
might be capable of breaking the black hole horizon, thus potentially violating
the weak cosmic censorship conjecture.
