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

TL;DR

This paper investigates how spin precession and orbital frequencies in Kerr-Newman spacetimes can distinguish between black holes and naked singularities, providing potential observational signatures through QPOs.

Contribution

It derives new closed-form expressions for spin precession and orbital frequencies in Kerr-Newman spacetimes, highlighting how charge and spin influence black hole and naked singularity distinctions.

Findings

Spin precession diverges near black hole horizons but remains finite for naked singularities except at the ring singularity.

Nodal precession frequency behavior differs markedly between black holes and naked singularities, including possible sign reversal.

Orbital and epicyclic frequencies are affected by charge, influencing the ISCO and QPO signatures.

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.