Oscillatory motion and QPO signatures around rotating short-hairy black holes: Bridging theory and observation

Current study deals with the test particles dynamics around a rotating short-hairy black hole. We explore how the parameter related to SH affect the motion of particles. This solution is characterized by parameters such as the black hole mass $M$, rotation parameter $a$, short hairy $q$ that measures the strength of the hair and a parameter $\alpha$. We derive analytical solutions for the radial profiles of the particular energy and the particular $L$ for stable circular orbits in the equatorial plane. In addition, using the $V_{eff}$ approach, we examine the stability of circular equatorial orbits and the forces that affect the particles. The radial and latitudinal harmonic oscillation frequencies are calculated as functions of the mass $M$, parameter $\alpha$, SH parameter $q$, and rotation parameter $a$. We also examine the main features of quasi-periodic oscillations of test particles in very close stable circular orbits. Specifically, we study precession effects such as the periastron precession and Lense–Thirring effect. We compare the results we obtained with those that correspond to the Kerr–Newman black hole. Our findings show that the motion of particles around the black hole is significantly influenced by the parameters of the black hole model.