Quasinormal Modes and Greybody Factors: Black Hole with a Dark Matter Halo

This study deals with the quasinormal modes and greybody factors of the static black hole surrounded by a dark matter halo. For this, the effective potential parameter for the scalar, vector and gravitational perturbations has been formulated for the black hole under consideration. In both the scalar and vector perturbation fields, we investigate the quasinormal modes of the static black hole with a dark matter halo and get the quasinormal frequencies by applying the 6th-order Wentzel-Kramers-Brillouin approximation method and circular null geodesic technique. To investigate the quasinormal frequency, we consider a variety of values for the dark matter halo parameters [Formula: see text] and [Formula: see text]. The analysis of greybody factors shows that the behavior depends on different parameters: when the multipole number [Formula: see text] increases the transmission curves are shifted toward higher frequencies, which confirms the increased scattering. On the other hand, the increase of the dark matter halo parameters [Formula: see text] and [Formula: see text] moves the greybody factor curves to lower frequencies, indicating a higher probability of transmission. Additionally, we provide strict bounds on the greybody factors for scalar perturbations and validate the impact of the parameters [Formula: see text], [Formula: see text], and [Formula: see text]. We have noticed that the quasinormal modes analysis shows that the combined effects of the parameters [Formula: see text] and [Formula: see text] result in a significant decrease in the real oscillation frequencies. At the same time, the size of the imaginary part is reduced, which means that the damping rate will be reduced and the ringdown signal will last longer.