Black Holes Immersed in Galactic Dark Matter Halo

Abstract: We analyze the quasinormal modes (QNMs) of scalar, electromagnetic, and Dirac test fields in the background of a black hole immersed in a galactic dark matter halo. The analytic black hole solution considered here is sourced by a physically motivated halo density profile that leads to a flat galactic rotation curve. Using the sixth-order WKB method with Pad\'e approximants, we compute the QNM spectra for various field spins and parameter values, and provide numerical data in tabulated form. In addition to the numerical analysis, we derive analytic expressions for the quasinormal frequencies in the eikonal limit and beyond, by means of an expansion in inverse powers of the multipole number. We also calculate the Unruh temperature perceived by a static observer in the halo-modified spacetime. Our results demonstrate that the presence of the dark matter halo leads to observable modifications in the QNM spectra only if the density or compactness of the galactic halo is extraordinary high, so that quasinormal ringing a reliable observable for testing the black hole geometry, even in the presence of galactic environments.