Testing Quantum-Corrected Black Holes with QPOs Observations: A Study of Particle Dynamics and Accretion Flow

Abstract: We study the epicyclic oscillations of test particles around rotating quantum-corrected black holes (QCBHs), characterized by mass $M$, spin $a$, and quantum deformation parameter $b$. By deriving the radial ($\Omega_r$) and vertical ($\Omega_\theta$) oscillation frequencies, we explore their dependence on spacetime parameters and show that quantum corrections ($b \neq 0$) significantly modify the dynamics compared to the classical Kerr case. Through numerical modelling of accretion around QCBHs, we further examine how $b$ influences strong-field phenomena, comparing the results with test-particle dynamics and observational data. Our analysis reveals: 1. Quantum corrections shift the ISCOs outward, with $b$ altering the effective potential and conditions for stable circular motion. 2. The curvature of the potential and thus the epicyclic frequencies change $\Omega_r$ shows up to 25% deviation for typical $b$ values, underscoring sensitivity to quantum effects. 3. Precession behavior is modified: while Lense-Thirring precession ($\Omega_{LT}$) remains primarily governed by $a$, periastron precession ($\Omega_P$) is notably affected by $b$, especially near the black hole. 4. Accretion disk simulations confirm the physical effects of $b$, aligning well with the test particle analysis. Moreover, quasi-periodic oscillation (QPO) frequencies obtained via both approaches agree with observed low-frequency QPOs from sources like GRS $1915+105$, GRO $J1655{-}40$, XTE $J1550{-}564$, and $H1743{-}322$. The distinct frequency profiles and altered ratios offer observational signatures that may distinguish QCBHs from classical black holes. Our findings present testable predictions for X-ray timing and a new avenue to constrain quantum gravity parameters.