  Compact bosonic field configurations, or boson stars, are promising dark
matter candidates which have been invoked as an alternative description for the
supermassive compact objects in active galactic nuclei. Boson stars can be
comparable in size and mass to supermassive black holes and they are hard to
distinguish by electromagnetic observations. However, boson stars do not
possess an event horizon and their global spacetime structure is different from
that of a black hole. This leaves a characteristic imprint in the
gravitational-wave emission, which can be used as a discriminant between black
holes and other horizonless compact objects. Here we perform a detailed study
of boson stars and their gravitational-wave signatures in a fully relativistic
setting, a study which was lacking in the existing literature in many respects.
We construct several fully relativistic boson star configurations, and we
analyze their geodesic structure and free oscillation spectra, or quasinormal
modes. We explore the gravitational and scalar response of boson star
spacetimes to an inspiralling stellar-mass object and compare it to its black
hole counterpart. We find that a generic signature of compact boson stars is
the resonant-mode excitation by a small compact object on stable quasi-circular
geodesic motion.
