Black Hole Quasi-Periodic Oscillations in the Presence of Gauss-Bonnet Trace Anomaly

Abstract: We investigate the effects of the Gauss-Bonnet (GB) gravitational trace anomaly on the circular motion of test particles around black holes (BHs) and its implications for quasi-periodic oscillations (QPOs) in various theoretical models. Beginning with the equations of motion, we study the effects on effective potential, angular momentum, specific energy, and the innermost stable circular orbit (ISCO) induced by the anomaly parameter $\alpha$. The fundamental frequencies are calculated. Moreover, we examine several QPO models, including PR, RP, WD, TD, and ER2-ER4, and study the relationship between the upper and lower QPO frequencies as well as the corresponding resonance radii for frequency ratios of 1:1, 3:2, 4:3, and 5:4. Our results show that increasing $\alpha$ leads to deviations from the Schwarzschild case in both upper and lower QPO frequencies correlations and QPO orbital radii, with model-dependent trends. Further, we constrain the BH parameters using the observational data using MCMC analysis. Finally, we calculate the upper and lower QPO frequencies for a few BH candidates on the basis of the RP model using the constrained parameter values and find a good agreement with the observed results.