Epicyclic Oscillations and Circular Orbits in Hairy Black Holes: Testing by High-Frequency Quasi-Periodic Oscillations Observed in Microquasars

Abstract

Recently, Ovalle and his collaborators proposed an exact solution to Einstein’s equations. In this study, we investigate the main characteristics of the spherically symmetric spacetime determined by the hair parameter l, with a specific focus on circular orbits, particularly the innermost circular orbits (ISCOs), and the epicyclic oscillatory motion along these orbits. To assess the validity of this novel geometry, we employ the frequencies derived from the epicyclic resonance model of high-frequency quasi-periodic oscillations (HF QPOs) observed in microquasars, as well as the ISCOs. By analyzing the observed data from three selected microquasars, we establish constraints on the parameter l. Our findings suggest that this geometric framework can encompass the phenomena associated with HF QPOs and offer a partial explanation for the observed shift in the ISCOs, which is commonly attributed to the rotation of the black hole.