Caio F. B. Macedo, Haroldo C. D. Lima, Raissa F. P. Mendes, Rodrigo Vicente, Vitor Cardoso

We investigate extreme-mass-ratio inspirals in which a stellar-mass compact object orbits a supermassive bosonic dark matter star, modeled as a boson star, using fully relativistic perturbative methods. Unlike inspirals around electro-vacuum black holes, these systems can shed scalar matter through dynamical friction which significantly alters the inspiral dynamics. We show that this additional dissipation can induce a chirp-like gravitational-wave signal closely resembling that of black hole binaries, allowing boson stars to act as gravitational-wave chirp mimickers even when they are not ultracompact. The inspiral evolution and resulting waveform depend sensitively on the compactness of the central boson star: highly compact configurations trigger dipolar scalar radiation, leading to a rapid plunge, whereas less compact stars yield smoother inspirals dominated by gravitational and quadrupolar scalar waves. To support waveform modeling, we derive semi-analytical prescriptions for the gravitational and scalar energy fluxes that remain accurate deep into the relativistic regime. Our findings indicate that future space-based detectors such as LISA could distinguish these mimicker signals from true black hole inspirals through measurable phase dephasings induced by scalar dissipation.