Geodesic motion in the space-time of a noncompact boson star

Abstract

We study the geodesic motion of test particles in the space-time of noncompact boson stars. These objects are made of a self-interacting scalar field and---depending on the scalar field's mass---can be as dense as neutron stars or even black holes. In contrast to the former these objects do not contain a well-defined surface, while in contrast to the latter the space-time of boson stars is globally regular and can---however---only be given numerically. Hence, the geodesic equation also has to be studied numerically. We discuss the possible orbits for massive and massless test particles and classify them according to the particle's energy and angular momenta. The space-time of a boson star approaches the Schwarzschild space-time asymptotically; however, it deviates strongly from it close to the center of the star. As a consequence, we find additional bound orbits of massive test particles close to the center of the star that are not present in the Schwarzschild case. Our results can be used to make predictions about extreme-mass-ratio inspirals, and we hence compare our results to recent observational data of the stars orbiting Sagittarius ${A}^{*}$---the radio source at the center of our own Galaxy.