Fundamental fields around compact objects: Massive spin-2 fields,
  Superradiant instabilities and Stars with dark matter cores
  Fundamental bosonic fields of arbitrary spin are predicted by generic
extensions of the Standard Model and of General Relativity, and are
well-motivated candidates to explain the dark components of the Universe. One
of most promising channels to look for their presence is through their
gravitational interaction with compact objects. Within this context, in this
thesis I study several mechanisms by which bosonic fields may affect the
dynamics and structure of black holes and neutron stars. The first part of the
thesis is devoted to the study of massive spin-2 fields around spherically
symmetric black-hole spacetimes. Massive spin-2 fields can be consistently
described within theories of massive gravity, making it possible to perform a
systematic study of the propagation of these fields in curved spacetimes. In
particular, I show that due to the presence of additional degrees of freedom in
these theories, the structure of black-hole solutions is richer than in General
Relativity. In the second part of the thesis, I discuss in detail superradiant
instabilities in the context of black-hole physics. I show that several
mechanisms, such as massive bosonic fields and magnetic fields, can turn
spinning black holes unstable against superradiant modes, which has important
implications for astrophysics and for physics beyond the Standard Model. In the
last part of this thesis, I present a study of how bosonic dark matter
condensates interact gravitationally with compact stars. In particular, I show
that stable stellar configurations formed by a perfect fluid and a bosonic
condensate exist and can describe the late stages of dark matter accretion onto
stars, in dark matter rich environments.
