Shadows and quasinormal modes of a Schwarzschild black hole immersed in Hernquist dark matter halo

This paper investigates the shadow and quasinormal modes (QNMs) of a Schwarzschild black hole (BH) embedded in a Hernquist dark matter (DM) halo, focusing on the influence of DM parameters – specifically the core radius rₛ r s and core density ρ ₛ ρ s – on BH observational signatures. We analyze the structure of the BH shadow, lensing ring, and photon ring, showing that the shadow radius increases with both rₛ r s and ρ ₛ ρ s . Using the WKB approximation, Padé approximants, and time-domain integration, we compute the QNMs for scalar, electromagnetic, and axial gravitational perturbations. Our results reveal that the DM halo modifies the spacetime’s effective potential: larger values of rₛ r s or ρ ₛ ρ s reduce the peak of the potential barrier, leading to lower oscillation frequencies and slower wavefunction damping. These findings highlight the systematic impact of DM on strong-field observables and suggest that BH shadows and QNMs provide a viable means to probe DM profiles in galactic nuclei.