Description
Compact astrophysical objects, like black holes and neutron stars, are
going to open a new and enlightening window on gravity in the
forthcoming years. The study of such objects in strong curvature
regimes will a priori allow to test alternative gravity theories, like
scalar-tensor models. I will discuss spherically symmetric and static
objects in the framework of Horndeski theory, proving the absence of
scalar hair for most models. I will also carefully classify the
possible ways to escape this no-hair theorem.