The Gravity of Classical Fields: And Its Effect on the Dynamics of
  Gravitational Systems
  Classical fields are ubiquitous in theoretical physics. They find
applications in almost all areas of physics, from condensed matter and particle
physics to cosmology and astrophysics. Scalar fields, in particular, can give
rise to confined structures, such as boson stars, oscillatons or Q-balls. These
objects are interesting hypothetical new "dark matter stars", but also good
descriptions of dark matter cores when the fields are ultralight. In this
thesis, we study the dynamical response of such confined bosonic structures
when excited by external matter (stars, planets or black holes) in their
vicinities. Such perturbers can either be piercing through the bosonic
configuration or undergoing periodic motion at its center (e.g., binaries). Our
setup can also efficiently describe the interaction between a moving massive
black hole and the surrounding environment. It also depicts dark matter
depletion as a reaction to an inspiralling binary within a dark matter core.
Our results provide a complete picture of the interaction between black holes
or stars and the ultralight dark matter core environment where they may live
in. This thesis also deals with several classical field environmental effects
on the motion (or, ultimately, the survival) of compact objects, like black
holes.
