Black strings and BTZ black holes sourced by a Dekel-Zhao dark matter profile

In this work, we obtain analytical solutions for a $(3+1)$-dimensional black string and a BTZ black hole, both sourced by the Dekel-Zhao dark matter (DM) density profile. Our results indicate that the event horizon radius is sensitive to the inner slope parameter $a$; specifically, beyond a critical threshold, the horizon vanishes, leading to the formation of naked singularities. We find that the DM environment induces curvature singularities in the Ricci and Kretschmann scalars, which are absent in the vacuum BTZ case. Furthermore, an analysis of the effective energy-momentum tensor shows that while the null, weak, and strong energy conditions are strictly satisfied, the dominant energy condition is violated in the BTZ scenario due to the high tangential pressure gradient. We also observe that DM modifies the Hawking temperature and free energy without compromising local or global stability. Notably, the DM distribution transforms the originally constant-curvature BTZ spacetime into a singular one, suggesting that a inherent stiffness of the DM profile is a determinant factor in the causal structure of these solutions.

💡 Research Summary

The authors investigate how a realistic dark‑matter (DM) density distribution, namely the Dekel‑Zhao (DZ) profile, modifies the geometry, energy conditions and thermodynamics of two non‑standard black objects: a (3+1)‑dimensional black string and a (2+1)‑dimensional BTZ black hole. Starting from the Einstein–Hilbert action with a negative cosmological constant (Λ = −3/ℓ²), they adopt a static, cylindrically symmetric metric for the black string, (ds^{2}= -f(r)dt^{2}+f^{-1}(r)dr^{2}+r^{2}d\phi^{2}+r^{2}\ell^{2}dz^{2}), and a similar form for the BTZ hole. The matter source is the DZ density (\rho(r)=\rho_{c}\left(\frac{r}{r_{c}}\right)^{-a}!\left