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

Abstract 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 $$r_{s}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>r</mml:mi> <mml:mi>s</mml:mi> </mml:msub> </mml:math> and core density $$\rho _{s}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>ρ</mml:mi> <mml:mi>s</mml:mi> </mml:msub> </mml:math> – 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 $$r_{s}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>r</mml:mi> <mml:mi>s</mml:mi> </mml:msub> </mml:math> and $$\rho _{s}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>ρ</mml:mi> <mml:mi>s</mml:mi> </mml:msub> </mml:math> . 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 $$r_{s}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>r</mml:mi> <mml:mi>s</mml:mi> </mml:msub> </mml:math> or $$\rho _{s}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>ρ</mml:mi> <mml:mi>s</mml:mi> </mml:msub> </mml:math> 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.