The S-stars, discovered in the vicinity of the massive black hole (MBH) in the Galactic center (GC), are anticipated to provide unique dynamical constraints on the MBH spin and metric, in addition to the mass. In this paper, we develop a fast full general relativistic method to simultaneously constrain the MBH mass, spin, and spin direction by considering both the orbital motion of a star close to the GC MBH and the propagation of photons from the star to a distant observer. Based on the current observations and dynamical model predictions, we assume six example stars with different semimajor axes (a orb ) and eccentricities (e orb ) and numerically calculate their projected trajectories in the sky plane and redshift curves. Two of those stars are set to have orbital configurations similar to that of S0-2/S2 and S0-102. We find that the spin-induced effects on the projected trajectory and redshift curve of a given star, including the leading term by the Lense-Thirring precession and the frame dragging, and the high-order precession due to the quadruple moment, depend on both the absolute value and the direction of the spin. The maximum values of the spin-induced position displacement and the redshift differences of the star over a full orbit may differ by a factor of several to more than one order of magnitude for two cases with significantly different spin directions. The dependence patterns of the position displacements and redshift differences on the spin direction are different, and thus the position and the redshift data are complementary for constraining the MBH spin and its direction. Adopting the Markov Chain Monte Carlo fitting technique, we illustrate that the spin of the GC MBH is likely to be well constrained by using the motion of S0-2/S2 over a period of ∼ 45 years if the spin is close to one and if the astrometric and spectroscopic precisions can be as high as (σ p , σ Z ) ∼ (10µas, 1km s −1 ), which is expected to be realized by future facilities like the GRAVITY on the Very Large Telescope Interferometer, the thirty meter telescope, and the European extremely large telescope. If σ p and σ Z can be further improved by a factor of several, the MBH spin can be well constrained by monitoring S0-2/S2 over a period of ∼ 15 years. In the mean time, the distance from the Sun to the GC and the MBH mass can also be constrained to an unprecedented accuracy (0.01%-0.1%). If there exists a star with a semimajor axis that is a few times smaller than, and eccentricity larger, than those of S0-2/S2, the MBH spin and its direction can be constrained with high accuracy over a period of < ∼ 10 year by future facilities, even if the spin is only moderately large. Our results suggest that long-term monitoring of the motions of stars in the vicinity of the GC MBH by the next generation facilities is likely to provide a dynamical test, for the first time, to the spin and metric of the GC MBH.

Hypervelocity stars (HVSs) escaping away from the Galactic halo are dynamical products of interactions of stars with the massive black hole(s) (MBH) in the Galactic Center (GC). They are mainly B-type stars with their progenitors unknown. OB stars are also populated in the GC, with many being hosted in a clockwise-rotating young stellar (CWS) disk within half a parsec from the MBH and their formation remaining puzzles. In this paper, we demonstrate that HVSs can well memorize the injecting directions of their progenitors using both analytical arguments and numerical simulations, i.e., the ejecting direction of an HVS is almost anti-parallel to the injecting direction of its progenitor. Therefore, the spatial distribution of HVSs maps the spatial distribution of the parent population of their progenitors directly. We also find that almost all the discovered HVSs are spatially consistent with being located on two thin disk planes. The orientation of one plane is consistent with that of the (inner) CWS disk, which suggests that most of the HVSs originate from the CWS disk or a previously existed disk-like stellar structure with an orientation similar to it. The rest of HVSs may be correlated with the plane of the northern arm of the mini-spiral in the GC or the plane defined by the outer warped part of the CWS disk. Our results not only support the GC origin of HVSs but also imply that the central disk (or the disk structure with a similar orientation) should persist or be frequently rejuvenated over the past 200 Myr, which adds a new challenge to the stellar disk formation and provides insights to the longstanding problem of gas fueling into massive black holes.