Shadow curves and quasinormal modes for rotating black holes surrounded by dark matter, radiation and dust (2504.18505v1)

Abstract: We study the impact of different fluid matter scenarios on the shadow of black holes (BH) and on frequencies of quasinormal modes (QNM) for a black hole subjected to scalar perturbations, with a comparison to the standard Kerr. The analysis of the shadow reveals a dependence on the density parameter of fluid matter $k$, with larger shadow sizes for larger values of $k$ in the dark matter and dust cases, while the shadow size becomes smaller in the radiation case. Notably, dark matter induces more visible deformations compared to radiation or dust, thereby highlighting its distinct imprint on shadow curves. We also find that dark matter reduces the real part of the QNM frequencies and significantly increases the damping time, enhancing the prospects for gravitational wave detection. The variations in spin parameter $a$, density parameter $k$ and multipole number $l$ are investigated. The analysis confirms the significant role of dark matter in modifying the behavior of QNMs, providing a promising avenue for future experiments.