Quasi-periodic oscillations in rotating and deformed space-times

Quasi-periodic oscillation (QPOs) analysis is important for understanding the dynamical behaviour of many astrophysical objects during transient events such as gamma-ray bursts, solar flares, magnetar flares, and fast radio bursts. In this paper, we analyse QPO data in low-mass X-ray binary (LMXB) systems, using the Lense-Thirring, Kerr, and approximate Zipoy-Voorhees metrics. We demonstrate that the inclusion of spin and quadrupole parameters modifies the well-established results for the fundamental frequencies in the Schwarzschild space-time. We interpret the QPO data within the framework of the standard relativistic precession model, allowing us to infer the values of the mass, spin, and quadrupole parameters of neutron stars in LMXBs. We explore recent QPO data sets from eight distinct LMXBs, assess their optimal parameters, and compare our findings with results in the existing literature. Finally, we discuss the astrophysical implications of our findings.