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General relativity predicts that black holes are described by the Kerrmetric, which has integrable geodesics. This property is crucial to produceaccurate waveforms from extreme-mass-ratio inspirals. Astrophysicalenvironments, modifications of gravity and new fundamental fields may lead tononintegrable geodesics, inducing chaotic effects. We study geodesics aroundself-interacting rotating boson stars and find robust evidence ofnonintegrability and chaos. We identify islands of stability around resonantorbits, where the orbital radial and polar oscillation frequency ratios, knownas rotation numbers, remain constant throughout the island. These islands aregenerically present both in the exterior and the interior of compact bosonstars. A monotonicity change of rotation curves takes place as orbits travelfrom the exterior to the interior of the star. Therefore, configurations withneutron-star-like compactness can support degenerate resonant islands. Thisanomaly is reported here for the first time and it is not present in blackholes. Such configurations can also support extremely prolonged resonantislands that span from the exterior to the interior of the star and areshielded by thick chaotic layers. We adiabatically evolve inspirals usingapproximated post-Newtonian fluxes and find time-dependent plateaus in therotation curves which are associated with island-crossing orbits. Crossings ofexternal islands give rise to typical gravitational-wave glitches found innon-Kerr objects. Furthermore, when an inspiral is traversing an internalisland that is surrounded by a thick chaotic layer, a new type of simultaneousmultifrequency glitch occurs that may be detectable with space interferometerssuch as LISA, and can serve as evidence of an extreme-mass-ratio inspiralaround a supermassive boson star.

Extreme-mass-ratio inspirals into rotating boson stars: nonintegrability, chaos, and transient resonances