Dark matter halo as a source of regular black-hole geometries

We construct exact black hole solutions free of curvature singularities, sourced by dark matter halos described by galactic density profiles. Regularity of the geometry is ensured by adopting the relation $P_{r}=-ρ$ between radial pressure and density, which is consistent with the phenomenological freedom of halo models. Under the assumptions of regularity and the weak-energy condition, sufficiently dense dark matter halos can give rise to asymptotically flat, singularity-free black holes embedded in a galactic environment. These regular black holes are shown to be stable under axial perturbations. In particular, we obtain solutions corresponding to Einasto and Dehnen-type dark matter profiles. We further compute the shadow radii and Lyapunov exponents associated with photon circular orbits around these black holes.