Signatures of a Schwarzschild-like Black Hole Immersed in Dark Matter Halo

Abstract

Astrophysical black holes are often surrounded by dark matter, which can influence their dynamics and observational signatures. In this work, we study a Schwarzschild-like black hole immersed in a Dehnen-type $(1,4,2)$ dark matter halo and analyse scalar, electromagnetic, and gravitational perturbations in this spacetime. We compute quasinormal modes (QNMs) using the Wentzel-Kramers-Brillouin (WKB) approximation method with Pad\'e approximants, investigate particle motion and photon trajectories, and use black hole shadow observations to place constraints on the halo parameters. We further examine the greybody factors associated with Hawking radiation for different perturbation spins. This combined analysis aims to understand how dark matter environments may affect black hole oscillations, radiation properties, and the corresponding observational signatures.