(keynote speaker)
Extreme mass-ratio inspirals into black holes surrounded by boson clouds
Boson clouds can form through superradiant instabilities of ultralight bosons around spinning black holes. The formation of boson clouds leads to a number of potentially detectable signatures, among them the possibility that they can affect the dynamics of binary black hole systems. After briefly reviewing the topic, I will present recent work aiming at studying extreme-mass-ratio systems in which a small compact object evolves around a supermassive black hole surrounded by a boson cloud. Most of the work on the subject typically assumed Newtonian approximations. By making use of tools from black hole perturbation theory, here we present the first steps towards studying those systems in a fully relativistic setup