Dyonic rotating cosmological black hole surrounded by quintessence

In this work, we constructed a new metric describing a rotating cosmological black hole with electric and magnetic charges in the presence of quintessence dark energy, where the cosmological constant and quintessence are associated with external matter. Starting from a Schwarzschild-type metric and considering all energy contributions in the function $f(r)$, we introduced rotation through the Newman–Janis algorithm using a unique and general complexification rule, avoiding possible ambiguities. Assuming that the metric satisfies the Einstein field equations with matter, we calculate the event horizon condition, the total stress–energy tensor $T_{\mu \nu }$, and the Kretschmann and Ricci scalars. We also analyze the influence of the cosmological constant $\mathrm{\Lambda }$ and quintessence parameter $\alpha$ on the event horizon and ergosphere. In the limit $\alpha \to 0$, the scalar curvature differs from the vacuum result, $R\mathrm{\ne }-4\mathrm{\Lambda }$, while the singularity region remains unchanged. Finally, we investigate the angular and rotational velocities of a test particle, as well as the energy conditions, through the energy density and pressures required for the existence of this black hole solution.