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 $ξ$ 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 $ξ$ 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 $ξ\leq 0.01869$ and $ξ\leq 0.73528$ 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 $ξ\leq 2.086$. 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.

Figures (4)

• Figure 1: The trajectories of a test particle moving in the equatorial plane ($z=0$) of a QCBH spacetime are shown for different values of the quantum correction parameter $\xi$. Left panel: The orbital motion of a particle with specific energy $\mathcal{E} = 0.992$, specific angular momentum $\mathcal{L} = 5$, and initial inverse radial coordinate $u = 1/r = 0.01$ around a black hole of mass $M=1$. Right panel: The effect of $\xi$ on the perihelion shift of a particle with $\mathcal{E} = 0.999$, $\mathcal{L} = 12.5$, and $u = 1/r = 0.01$. As $\xi$ increases, the perihelion shift decreases, highlighting the impact of quantum corrections on the orbital dynamics.
• Figure 2: The radial profile of the frequencies $\nu_\theta$ and $\nu_r$ measured by a distant observer is shown as a function of $r/M$ for different values of the quantum correction parameter $\xi$.
• Figure 3: Left: The upper $\nu_U$ frequency is depicted as functions of the mass $M$ for different values of the quantum correction parameter $\xi$, analyzed near the innermost stable circular orbit $r_{\text{isco}}$. Red horizontal lines indicate the observational data for various QPO sources, with the width of these lines representing the uncertainty in the mass of the sources. Right: The upper and lower frequencies of a particle near the innermost stable circular orbit $r_{\text{isco}}$ are plotted as function of $M/M_\odot$ for the best-fit values of the quantum correction parameter $\xi$. The black solid curve represents the best-fit curve of the upper frequency $f_U$, while the blue solid curve corresponds to the lower frequency $f_L$. Observational data for various QPO sources are shown as horizontal lines, where red lines indicate the upper frequency and green lines represent the lower frequency. The width of these horizontal lines reflects the uncertainty in the mass estimates of the sources.
• Figure 4: Constraints on the parameters of QCBH from QPO observations of GRO J1655-40, GRS 1915+105, H1743-322, and XTE J1550-564 using the MCMC method. The plots show the posterior distributions for the black hole mass $M$, the dimensionless radius $r/M$, and the quantum correction parameter $\xi$ within the forced resonance mode. The vertical dashed red lines indicate the 95% confidence level for $\xi$.