Inertial Frame Dragging as a Probe to Differentiate Kerr-Newman Naked Singularities from Black Holes

Abstract

We study the spin precession of a test gyroscope attached to a stationary observer in Kerr-Newman spacetime to distinguish a naked singularity from a black hole. Extending earlier work on Kerr, we examine how the electric charge \(Q\) affects precession in both cases. For gyroscopes with nonzero angular velocity \(\Omega\), we derive closed-form expressions for the general spin-precession, Lense-Thirring, and geodetic precession frequencies. For Kerr-Newman black holes, the spin-precession frequency generically diverges as the event horizon is approached from any direction, remaining finite only for zero-angular-momentum observers (ZAMOs). By contrast, for Kerr-Newman naked singularities, it remains finite everywhere except at the ring singularity on the equatorial plane. We show that \(Q\) systematically modifies these features, especially in rapidly rotating regimes, and that the acceleration scalar further sharpens the black hole/naked singularity distinction. We also investigate the Lense-Thirring (nodal) precession frequency of equatorial circular orbits in accretion disks. For black holes, the nodal frequency decreases monotonically with radius, whereas for naked singularities it rises, attains a finite maximum, and then decreases; for sufficiently large spin and charge it can even change sign, signalling a reversal of the precession direction. We further compute the Keplerian, radial, and vertical epicyclic frequencies, along with the periastron precession frequency, highlighting the role of \(Q\) in the ISCO and the orbital-frequency hierarchy. Since these frequencies are closely related to observed quasiperiodic oscillations (QPOs), these features provide a strong-field probe of whether a rotating compact object is a black hole or a naked singularity.