Topological analysis of novel charged-AdS black hole solutions embedded in dark matter halos with quintessence field
In this work, we investigate the properties of a charged anti-de Sitter (AdS) black hole in the presence of a NGC 4649-type dark matter halo and a surrounding quintessence field. Starting from the modified Einstein field equations (EFEs), we construct the corresponding black hole solutions by incorporating the effects of electric charge, cosmological constant, dark matter distribution, and quintessence characterized by a variable equation of state. We analyze the resulting spacetime geometry through the metric function and horizon structure, showing that the dark matter halo strengthens the gravitational attraction, whereas the quintessence field provides a repulsive contribution that substantially alters the asymptotic behavior of the spacetime. Furthermore, the thermodynamic properties are investigated by applying the Duan-\(ϕ\)-mapping topological theory together with the generalized free energy method. This framework allows us to examine the topological structure, critical behavior, and stability conditions of the black hole system in a consistent manner. We further study the fractional shifts relative to the reference value of \(ω_q\) and observe that variations in \(ω_q\) produce systematic changes which highlight the important role of the quintessence field in determining the phase structure and critical behavior of the black hole system.