Quasinormal modes of black holes embedded in halos of matter

We investigate the (axial) quasinormal modes of black holes embedded in generic matter profiles. Our results reveal that the axial QNMs experience a redshift when the black hole is surrounded by various matter environments, proportional to the compactness of the matter halo. Our calculations demonstrate that for static black holes embedded in galactic matter distributions, there exists a universal relation between the matter environment and the redshifted vacuum quasinormal modes. In particular, for dilute environments the leading order effect is a redshift $1+U$ of frequencies and damping times, with $U\sim -\mathcal{C}$ the Newtonian potential of the environment at its center, which scales with its compactness $\mathcal{C}$.