Comment on "Black hole in Dehnen $(1,\,4,\,\frac{1}{2})$ dark matter halo: exact solution, lensing, light ring, and thermodynamics (EPJC 85 (2025) 1256)"

Abstract

In a recent article, the author of Ref. [EPJC 85 (2025) 1256] constructed an exact solution describing a static, spherically symmetric black hole embedded in a Dehnen-($\alpha, \beta, \gamma$) type dark matter halo with the parameter choice $\alpha=1,\,\beta=4,\,\gamma=1/2$. The author first derived the density profile, which was subsequently integrated to obtain the mass profile, and this mass profile was then employed in constructing the exact metric solution. In this comment, we demonstrate that both the density profile and the mass profile obtained in Ref. [EPJC 85 (2025) 1256] contain fundamental mathematical errors that invalidate the subsequent analysis.