Future space-borne gravitational-wave detectors will observe the gravitational waves in the milli-Hz. Extreme-mass-ratio inspirals with central supermassive black holes are very important sources that could provide the information of the vicinity of
black holes. The event horizon separates the inner region of a black hole and there is nothing that can escape from this region. When the central supermassive compact object is a regular and horizonless rotating boson star, a small body could pass through the center and follow novel types of orbits. These will generate the gravitational waves that can not be obtained in the scenario corresponding to an extreme-mass-ratio inspiral with a central supermassive black hole. This can be used to examine whether a supermassive rotating boson star is present at the centers of galaxies. In this work, we consider an extreme-mass-ratio inspiral system described by a small compact object inspiralling into a central supermassive rotating boson star. Integrating four types of special equatorial geodesics and using the numerical kludge method with quadrupole approximation, we obtain the corresponding gravitational waveforms and find that there are high-frequency gravitational radiation pulses in such system. The frequencies of the gravitational radiation pulses could be in the magnitude of $10^{-1}$Hz and the whole gravitational wave parts are in the milli-Hz. By assuming the masses of the central supermassive rotating boson star and small compact object to be $10^6 M_odot$ and $10 M_odot$ and assuming a distance of $1text{Gpc}$, we show that the gravitational radiation pulses could be detected by the space-borne gravitational-wave detectors. Our results will provide a possible evidence to distinguish the astrophysical compact objects in the galactic centers.
Motion of a test particle plays an important role in understanding the properties of a spacetime. As a new type of the strong gravity system, boson stars could mimic black holes located at the center of galaxies. Studying the motion of a test particl
e in the spacetime of a rotating boson star will provide the astrophysical observable effects if a boson star is located at the center of a galaxy. In this paper, we investigate the timelike geodesic of a test particle in the background of a rotating boson star with angular number $m=(1, 2, 3)$. With the change of angular number and frequency, a rotating boson star will transform from the low rotating state to the highly relativistic rapidly rotating state, the corresponding Lense-Thirring effects will be more and more significant and it should be studied in detail. By solving the four-velocity of a test particle and integrating the geodesics, we investigate the bound orbits with a zero and nonzero angular momentum. We find that a test particle can stay more longer time in the central region of a boson star when the boson star becomes from low rotating state to highly relativistic rotating state. Such behaviors of the orbits are quite different from the orbits in a Kerr black hole, and the observable effects from these orbits will provide a rule to investigate the astrophysical compact objects in the Galactic center.
