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arXiv · 2605.26198

Black string immersed in perfect fluid dark matter

L. G. Barbosa·L. C. N. Santos
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Abstract

We present an exact four-dimensional black string solution immersed in perfect fluid dark matter within an anti-de Sitter background. By solving the Einstein field equations for an anisotropic fluid, we obtain a metric function that modifies the standard black string geometry through a logarithmic term governed by the dark matter parameter $\alpha$. The event horizon radii are analytically determined using the Lambert $W$ function, and the Kretschmann scalar confirms a genuine curvature singularity at the origin alongside the expected asymptotic behavior. Furthermore, we evaluate the thermodynamic properties of the solution. The heat capacity diverges at a critical horizon radius for $\alpha>0$, a behavior commonly associated with a thermodynamic phase transition in a regime where the weak energy condition is violated.

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L. G. Barbosa, L. C. N. Santos. 2026-05-25. Black string immersed in perfect fluid dark matter. https://arxiv.org/abs/2605.26198

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