  Fundamental fields are a natural outcome in cosmology and particle physics
and might therefore serve as a proxy for more complex interactions. The
equivalence principle implies that all forms of matter gravitate, and one
therefore expects relevant, universal imprints of new physics in strong field
gravity, such as that encountered close to black holes. Fundamental fields in
the vicinities of supermassive black holes give rise to extremely long-lived,
or even unstable, configurations which slowly extract angular momentum from the
black hole or simply evolve non-linearly over long timescales, with important
implications for particle physics and gravitational-wave physics. Here, we
perform a fully non-linear study of scalar-field condensates around rotating
black holes. We provide novel ways to specify initial data for the
Einstein-Klein-Gordon system, with potential applications in a variety of
scenarios. Our numerical results confirm the existence of long-lived bar-modes
which act as lighthouses for gravitational wave emission: the scalar field
condenses outside the black hole geometry and acts as a constant frequency
gravitational-wave source for very long timescales. This effect could turn out
to be a potential signature of beyond standard model physics and also a
promising source of gravitational waves for future gravitational wave
detectors.
