Modeling the Sgr A* Black Hole Immersed in a Dark Matter Spike.

In this paper, we investigate the effects of a dark matter (DM) spike on the neighborhood of Sgr A*, the black hole (BH) in the center of the Milky Way. Our main goal is to investigate whether current and future astronomical observations of Sgr A* could detect the presence of such a DM spike. At first, we construct the spacetime metric around a static and spherically symmetric BH with a DM spike, and later, this solution is generalized for a rotating BH using the Newman–Janis–Azreg-Aďnou algorithm. For the static BH metric, we use the data of the S2 star orbiting Sgr A* to determine and analyze the constraints on the two free parameters characterizing the density and innermost boundary of the DM halo surrounding the BH. Furthermore, by making use of the available observational data for the DM spike density ρ_sp and the DM spike radius R_sp in the Milky Way, we consider a geometrically thick accretion disk model around the Sgr A* BH and demonstrate that the effect of DM distribution on the shadow radius and the image of the BH is considerably weak for realistic DM densities, becoming significant only when the DM density is of the order ρ_sp ∼ (10⁻¹⁹–10⁻²⁰) g cm⁻³ near the BH. We further analyze the possibility of observing this effect with radio interferometry, simulating observations with an EHT-like array, and find that it is unlikely to be detectable in the near future. [ABSTRACT FROM AUTHOR]