Ariadna Uxue Palomino Ylla, Kosuke Makino, Akane Tanaka, Akihiro Ishibashi, Chul-Moon Yoo

We derive general formulas for quasi-normal mode (QNM) frequencies of hairy black holes by exploiting the QNM--geodesic correspondence. The black hole hair is treated as an anisotropic fluid perturbatively added to the vacuum black holes (Schwarzschild and Kerr black holes). Under this setting, independent of energy conditions, our formulas offer a systematic method to compute quasi-normal mode frequencies for a broad class of hairy black holes.