Motion in time-periodic backgrounds with applications to ultralight dark
  matter haloes at galactic centers
  We consider motion in spherically symmetric but time-dependent backgrounds.
This problem is of interest, for example, in the context of ultralight dark
matter, where galactic haloes produce a time-dependent and periodic
gravitational potential. We study the properties of motion of stars in such
spacetimes, for different field strengths and frequency, and including
dissipative effects. We show that orbital resonances may occur and that
spectroscopic emission lines from stars in these geometries exhibit
characteristic, periodic modulation patterns. In addition, we work out a fully
relativistic and weak-field description of a special class of time-periodic
geometries, that of scalar oscillatons. When applied to the galactic center,
our results indicate that the motion of S2-like stars may carry distinguishable
observational imprints of ultra-light dark matter.
