Quasi-normal modes of rotating black holes beyond General Relativity

In this talk, I will summarize the recent advancements of quasi-normal modes in alternative theories of gravity. I will explain the main issues in computing the characteristic frequencies of rotating black holes and what are the most prominent strategies to tackle this problem.

The approaches covered include the slow-spin and small-coupling expansions. In particular, I will present a beyond-Teukolsky approach for the computation of quasi-normal modes using the continued fraction method, and its application in several modified theories of gravity.