Spin precession frequencies of a test gyroscope around a naked singularity and quasi-periodic oscillations

Various studies show that the gravitational collapse of inhomogeneous matter clouds leads to naked singularity formation. We investigate here the spin precession frequency of a test gyroscope attached to a stationary observer in a rotating naked singularity spacetime. In the weak field limit, Lense-Thirring precession for rotating naked singularity and geodetic precession in asymptotic limit for null naked singularity are found to be equal to that of a Kerr black hole and a Schwarzschild black hole respectively. In addition, we can distinguish rotating naked singularity and Kerr naked singularity for an observer in the equatorial plane using spin precession. To this end, we have found the constraints on the parameters of rotating naked singularity by employing Monte Carlo Markov Chain simulation and using the observation from five quasi-periodic sources within the relativistic precession model. Our analysis shows that the measurement of spin parameter estimate for GRO J1655-40 is in disagreement with the value found from the continuum-fitting method, while for XTEJ1859+226 and GRS 1915+105, it is inconsistent with spectral analysis results.