Boson stars in Bumblebee gravity and their gravitational waveforms from extreme-mass-ratio inspirals

We investigate the impact of Lorentz violation on the compactness of mini-boson stars and the resulting gravitational-wave signals from extreme-mass-ratio inspirals (EMRIs) within the framework of bumblebee gravity. Numerical solutions for static, spherically symmetric configurations reveal that a positive Lorentz-violating parameter ℓ suppresses repulsive pressure, thereby enhancing gravitational binding and yielding more compact boson stars. Conversely, a negative ℓ amplifies repulsive pressure and weakens gravitational binding, such that no static solutions exist beyond a critical negative value. These structural modifications imprint distinct features on EMRI dynamics, characterized by a monotonic decrease in both orbital eccentricity and radial range as ℓ gradually increases from negative to positive values. Unlike the intermittent bursts from grazing orbits that resemble black-hole signals, penetrating orbits that enter the boson-star core exhibit sustained, amplitude-modulated gravitational-wave signatures without quiet intervals. Their characteristic strain falls within the detectability range of LISA, providing a potential observable for constraining Lorentz violation.