Probing quantum corrected black hole through astrophysical tests with the orbit of S2 star and quasiperiodic oscillations

Abstract: In this study, we explore the influence of the quantum correction parameter $\xi$ on the motion of particles and the properties of quasiperiodic oscillations (QPOs) around a quantum-corrected black hole (QCBH). We first analyze the geodesics of a test particle and derive weak-field constraints on parameter $\xi$ from the perihelion precession of orbits, using observations from the Solar System and the S2 star's orbit around $\text{SgrA}^\star$ supermassive black hole in the center of our galaxy. We obtain $\xi \leq 0.01869$ and $\xi \leq 0.73528$ using the analysis of Solar System observations and the orbit of the S2 star around $\text{SgrA}^\star$, respectively. In the strong-field regime, we examine the dynamics of epicyclic motion around astrophysical black holes and, using observational data from four QPO sources and the Markov Chain Monte Carlo (MCMC) method, we determine the upper constraint $\xi \leq 2.086$. Our results provide new insights into the effects of quantum corrections on black hole spacetimes and highlight the potential of QPOs as a probe for testing quantum gravity in astrophysical environments.