Periodic gravitational lensing by oscillating boson stars

We show that oscillating (real-scalar) boson stars can act as strictly periodic gravitational lenses and generically host an \emph{oscillating radial caustic}. Sources near this caustic cross it every half period, producing achromatic phase-locked photometric spikes synchronized with an astrometric wobble, providing a promising target for time-domain astronomy. Event-number estimation indicates a measurable discovery space with current astrometric and high-cadence photometric surveys. These predictions rely only on the dynamics of long-lived real-scalar condensates, therefore offering a clean test of self-gravitating quantum fields in curved spacetime. The framework extends naturally to self-interacting real scalars (including axion-like particles) and to ultralight vector bosons.