Probing Hairy Kerr Black Holes through Quasi-Periodic Oscillations I: A study based on the kinematic models

Abstract: Black hole (BH) solutions endowed with nontrivial scalar or matter fields - commonly known as hairy black holes - have attracted significant interest in recent years. They admit extra parameters beyond mass, charge, and angular momentum, leading to a richer phenomenology. Characterizing their allowed parameter space is therefore crucial, especially in light of the available data from electromagnetic and gravitational-wave observations. The rotating hairy black hole solutions studied here are inspired by the gravitational decoupling method and satisfy the Einstein field equations with a conserved energy-momentum tensor that respects the strong energy conditions (SECs). We explore in detail the horizon structure of such black holes and report for the first time certain unique features, not observed in Kerr BHs. We investigate the sensitivity of the hairy parameters on the fundamental frequencies associated with the motion of matter in the hairy Kerr spacetime, and compare them with the Kerr scenario. The theoretical models aimed to explain the observed high-frequency observations (HFQPOs) in BHs are associated with the fundamental frequencies. Hence, such a study enables us to constrain the parameter space of the hairy Kerr spacetime by comparing the model-dependent HFQPO frequencies with the available observations. By comparing the kinematic models of HFQPOs with the observations of six BH sources, we report the most favored parameter space for each of these BHs. Our analysis also provides a framework to discern the most suitable model for each of these sources. Interestingly, even with the present precision of the data, the Relativistic Precession Model seems to be less suitable compared to the Tidal Disruption Model for the sources GRO J1655-40 and XTE J1859+226. The implications are discussed.