Influences of perfect fluid dark matter on coinciding validity of the weak gravity and weak cosmic censorship conjectures for Kerr-Newman black hole

One of the main difficulties in general relativity is the potential conflict between the weak gravity conjecture (WGC) and weak cosmic censorship conjecture (WCCC). Cosmic censorship is a basic assumption that guarantees the coherence of the gravity theory. However, this paper examines the feasibility of harmonizing the WGC and the WCCC by studying the Kerr Newman black hole surrounded by perfect fluid dark matter (PFDM) in asymptotically flat spacetimes. These two conjectures appear to be unrelated, but a recent idea proposed that they have a surprising connection. Specifically, we present a plausible set of for the WCCC in the four-dimensional framework, considering a Kerr-Newman black hole when WGC is active. We show that by applying certain restrictions on the parameters of the metric, the WGC and the WCCC can be consistent. Moreover, we explore the characteristics of the Kerr Newman black hole in the presence of PFDM for $Q>M$ and display some fascinating figures to verify the accuracy of the WGC and the WCCC at the same time. When PFDM is absent ($\lambda =0$), the Kerr Newman black hole has either two event horizons if $Q^2/M^2\le 1$, or none if $Q^2/M^2>1$. The latter case leads to a naked singularity, which violates the WCCC. But when PFDM is present ($\lambda \ne 0$), the Kerr Newman black hole has event horizons depending on Q, a, and M. This means that the singularity is always hidden, and the WGC and the WCCC are satisfied. Furthermore, we prove that there is a critical value of λ, denoted by ${\lambda }_{ext}$, that becomes the extremality Kerr Newman black hole when $\lambda ={\lambda }_{ext}$. In this case, the black hole has an event horizon, and the WGC and the WCCC are still satisfied. We conclude that PFDM can make the WGC and the WCCC compatible for the Kerr Newman black hole and that the WGC and the WCCC concur with each other when PFDM is present.