Long-lived quasinormal modes, grey-body factors and absorption cross-section of the black hole immersed in the Hernquist galactic halo

We analyze quasinormal modes, grey-body factors, and absorption cross-sections of a massive scalar field in the background of a Schwarzschild black hole surrounded by a Hernquist dark-matter halo. The quasinormal spectrum is obtained through the higher-order WKB method and verified by time-domain evolution, showing consistent results. The field mass increases the oscillation frequency and reduces the damping rate, producing longer-lived modes, while variations in the halo parameters lead to moderate shifts in the spectrum. The grey-body factors reveal a suppression of low-frequency transmission and a displacement of their main features toward higher frequencies, resulting in a corresponding shift in the absorption cross-section.