Long-lived quasinormal modes and grey-body factors of supermassive black holes with a dark matter halo

Abstract: We study quasinormal modes and grey-body factors of a massive scalar field in the background of a Schwarzschild black hole surrounded by a spherically symmetric galactic dark matter halo. The background metric, recently obtained as an analytic generalization of the Schwarzschild geometry, depends on the halo velocity parameter $V_{c}$ and the core radius $a$. Using the sixth- and seventh-order WKB methods with Pade approximants, supported by time-domain integration and Prony analysis, we compute the fundamental quasinormal frequencies and transmission coefficients. The results show that the real part of the frequency slightly increases while the damping rate decreases with growing field mass $μ$, leading to longer-lived oscillations. The influence of the dark matter halo parameters is found to be negligible for astrophysically realistic values, confirming the robustness of Schwarzschild-like ringdown signatures. Grey-body factors decrease with increasing field mass and multipole number, while the effect of the halo parameters remains small.