Dark Matter Imprints on Black Hole Shadows and Chaotic Dynamics: A Comparative Study of Halo Profiles around Sgr A and M87

Abstract

The gravitational influence of dark matter (DM) halos on the strong-field regime around supermassive black holes (SMBHs) remains largely unexplored. In the present work, we try to make a framework of the halo-modified space times for four well-known DM profiles including the Navarro Frenk-White (NFW), Moore, Burkert, and Dehnen-(1,4,3/4) profiles, respectively. We derive the corresponding photon spheres, shadow radii, and innermost stable circular orbits (ISCO) for the Sgr A* and M87*. We then constrain the DM halo parameters by comparing the theoretical values with the observed Event Horizon Telescope (EHT) data, and the robustness was checked by comparing the obtained virial mass of the Milky Way and M87 from the parameters with the values already present in the literature. In addition to this we extend the geodesic analysis by formulating the perturbed orbital dynamics using a Painlevé-Gullstrand Hamiltonian framework, and as a result we compute orbital trajectories, Poincaré sections, and finite-time Lyapunov ex ponents. These chaotic dynamics leave distinct imprints on gravitational waveforms, including phase irregularities and amplitude modulations.