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)"

TL;DR

This paper critically examines a recent exact solution for a black hole in a Dehnen dark matter halo, identifying fundamental mathematical errors in the original density and mass profiles that undermine its conclusions.

Contribution

It provides a detailed critique highlighting errors in the previous work's derivation of density and mass profiles, questioning the validity of its results.

Findings

Identification of fundamental errors in the density profile

Detection of inaccuracies in the mass profile derivation

Questioning of the original analysis validity

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.