The accretion of matter onto a black hole or a compact object is a classic problem but the case where the accreting matter is not ordinary matter but dark matter has been somewhat less studied. In the cosmological setting, a scenario which has recently attracted a renewed interest is that of ultralight dark matter (such as axion-like particles). In this internship we will consider the accretion within the framework of such dark matter models with non-negligible repulsive self-interactions. The study of the accretion onto a static black hole (Schwarzschild metric) has already been studied. However, black holes usually have a nonzero rotation (Kerr metric). The objective of the internship is thus to compute the accretion of the dark matter in the case of a rotating black hole. Such studies are also partly motivated by the detection of gravitational waves emitted by black hole binary systems, which can be modified by the matter environment of the black holes. This is a theoretical internship, which will involve both analytical and numerical works (Fortran, Python, Mathematica). The student will learn and use basics of black hole accretion and ultralight dark matter scenarios, the analytical and numerical study of partial differential equations and hydrodynamical codes (AMRVAC). A strong interest in both analytical and numerical works is required.