Inferring a spinning black hole in an expanding universe via the S2 star around the galactic center*

Abstract The nearest black hole to Earth, Sagittarius A (Sgr A ), with its intense gravitational field, provides a unique opportunity to explore black hole mysteries. Over the past few decades, monitoring of the S2 star has provided extensive valuable data that can be utilized to examine various gravity theories and black hole paradigms. This paper focuses on the most intriguing objects in astronomy, spinning black holes, and investigates the effects of spin on orbital motion. By applying the Markov Chain Monte Carlo algorithm to publicly available observational data of the S2 star, our findings indicate that current data fail to constrain the spin of Sgr A . Simulated stars with smaller semi-major axes reveal that the direction of Lense-Thirring precession aligns with the spin direction of Sgr A . Additionally, by incorporating the cosmological constant, which accounts for the expansion of the universe, into our analysis, we establish an upper limit of on the cosmological constant at the confidence level. Future long-term monitoring of S-cluster stars, combined with enhanced observational precision, may enable the determination of the spin of Sgr A and further tighten the bound on the cosmological constant.