Equatorial orbits of spinning test particle in rotating boson star

Abstract

In this paper, we study the circular orbit of the spinning test particle in the background of a rotating boson star. Using the pole-dipole approximation and neglecting the back-reaction of the spinning test particle on the spacetime, the equation of motion of the spinning test particle is described by the Mathisson-Papapetrou-Dixon equation. We solve this equation under the Tulczyjew spin-supplementary condition and obtain the four-momentum and four-velocity of the spinning test particle. Quite different from the spinless particle, the effective potential of the spinning particle with zero orbital angular momentum goes to infinite at the center of the rotating boson star. This will lead to the fact that the spinning particle can not pass through the center of the boson star. However, when the spin angular momentum and orbital angular momentum satisfy $2\bar{s}+\bar{l}=0$, the effective potential is not divergent anymore and the spinning particle can pass through the center of the rotating boson star. {We still investigate how the spin affects the structure of the circular orbits and we find that the spin will induce the larger or smaller regions of no circular orbits, unstable circular orbits, and stable circular orbits.} Moreover, the radius and energy of the circular orbit will be decreased or increased by the particle spin. These results will have an important application in testing the gravitational waves in the boson star background.

11 pages, 6 figures

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