Observational constraints on the Kerr and its several single-parameter modified spacetimes using quasi-periodic oscillation data

This paper investigates the dynamical effects of particles moving in the Kerr spacetime and its nine single-parameter modified spacetimes, including Bardeen, Ayon-Beato and Garcia (ABG), Hayward, Kerr-Newman (KN), Kerr-Taub-NUT (KTN), Braneworld Kerr (BK), Kerr-MOG, Kerr-Sen, and Perfect Fluid Dark Matter (PFDM) black holes. Using quasi-periodic oscillation (QPO) observational data, we constrain the free parameters of the ten spacetimes through $\chi^2$ analysis under the relativistic precession model of QPO. We constrain the modification parameters for the nine single-parameter modified spacetimes and provide the spin and mass ranges of three microquasars within the ten spacetime models (including Kerr) at the $68\%$ confidence level (CL). The results demonstrate that, at the $68 \%$ CL, the QPO data impose stringent constraints on the free parameters, as evidenced by the narrow confidence intervals. Among them, only the KN spacetime yields a modification parameter constraint spanning both negative and positive values (encompassing the Kerr case at zero). In contrast, all other tested geometries mandate positive-definite parameters at $68 \%$ CL, demonstrating statistical deviation of the Kerr solution. This highlights the significance of exploring modifications to the Kerr spacetime. Finally, we evaluate the spacetime models using the Bayes factor and the Akaike Information Criterion (AIC). Based on the current QPO observational data, the Bayesian factor analysis indicates that the ABG, Hayward, KN, BK, and Kerr-MOG spacetime have a slight advantage over the Kerr solution, while the Bardeen, KTN, Kerr-Sen, and PFDM spacetime are somewhat inferior to the Kerr model. In contrast, the AIC analysis shows that the Kerr spacetime remains the optimal model under the current QPO data.