Comment on "Effect of perfect fluid dark matter..." [Phys. Dark Univ. 34 (2021) 100891]

Abstract

This Comment clarifies the physical interpretation of the black hole spacetime metric employed by Shaymatov \textit{et al.} [Phys. Dark Univ. 34 (2021) 100891]. We point out that the metric, originally derived in Li and Yang (2012), describes a specific dual-component system consisting of cold dark matter and a phantom field background. Treating this geometry as a single-component ``Perfect Fluid Dark Matter'' (PFDM) with a total equation of state $w_{\mathrm{total}} = -1$ is physically incompatible with the gravitational attraction required for dark matter halos. Furthermore, we clarify the distinct parameter regimes of the original model to prevent potential misapplications in extreme astrophysical scenarios.