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

Abstract

We investigate inertial frame dragging and relativistic precession in the Kerr--Newman spacetime and show how gyroscopic observables can operationally discriminate between Kerr--Newman black holes and Kerr--Newman naked singularities. We study a test gyroscope attached to a stationary observer and derive closed-form expressions for the Lense--Thirring, geodetic, and general spin-precession frequencies. A sharp qualitative distinction emerges: for Kerr--Newman black holes, the spin-precession frequency generically diverges as the horizon is approached (remaining finite only for the ZAMO family), whereas for Kerr--Newman naked singularities, the precession remains finite throughout the spacetime, with divergences confined to the ring singularity on the equatorial plane. Working with physically admissible stationary observers (including ZAMOs), we first construct the timelike geodesic motion and the fundamental orbital frequencies for equatorial circular orbits. Using these, we analyse the radial and vertical epicyclic frequencies, the ISCO shift induced by the charge parameter $Q$, and the associated periastron and nodal precession frequencies relevant to quasi-periodic oscillations (QPOs). We demonstrate that nonzero $Q$ produces systematic, and in rapidly rotating regimes nontrivial, modifications to the frequency hierarchy: $ν_{\rm nod}$ can develop a finite maximum at $r=r_p=\mathcal{O}(M)$, its peak amplitude decreases with increasing $Q$, and sign reversals may occur for sufficiently large charge and high spin, signalling a reversal of nodal-precession orientation. These results establish spin-precession behaviour as a robust strong-field probe of horizons versus exposed singularities, with potential implications for testing cosmic censorship using future high-precision precession/QPO measurements.

Figures (20)

• Figure 1: Illustration showing the spin-charge parameter plane of a rotating Kerr-Newman spacetime. In Fig. (a), the curve separates the black hole region from the naked singularity region, corresponding to configurations without an event horizon. Fig. (b) represents the three-dimensional visualisation of the black hole with inner and outer event horizons.
• Figure 2: Illustration showing the variation of the orbital velocity $\Omega$ (in units of $M^{-1}$) of a test gyroscope as a function of the radial coordinate $r$ (in units of $M$) for different $Q$ values in the background of a rotating Kerr-Newman black hole, specifically within the ergoregion, restricted to the equatorial plane. The diverging red curve (solid and dotted) in all panels corresponds to the value of $\Omega_{\pm}$ in the naked singularity region. The behaviour of the curves clearly distinguishes the black hole configuration from the naked singularity case through the divergence of the orbital velocity near the central region.
• Figure 3: Vector field representation of the $\vec{\Omega}_{LT}$ precession frequency in the Cartesian plane corresponding to $(r, \theta)$. Panels (a), (c), and (e) depict the vector field for black holes, whereas panels (b), (d), and (f) correspond to naked singularities. The field lines show that, for black holes, the vector field is confined outside the ergosphere, while for naked singularities it remains finite and extends up to the ring singularity. The vectors form closed or elliptical loops, illustrating the rotational influence of spacetime and the characteristic frame-dragging effect induced by the black hole.
• Figure 4: Illustration showing the variation of the magnitude of $|\vec{\Omega}_{LT}|$ (in units of $M^{-1}$) precession frequency versus radial coordinate $r$ (in units of $M$) for different parameters. Panels (a), (c), and (e) depict the magnitude of Lense-Thirring precession frequency for black holes, whereas panels (b), (d), and (f) correspond to naked singularities.
• Figure 5: Variation of the geodetic precession frequency, $\Omega_{\mathrm{geodetic}}$ (in units of $M^{-1}$), with radial coordinate $r$ (in units of $M$) for different charge values $Q$ in a static charged black hole spacetime. Panels (a)--(b) show that $\Omega_{\mathrm{geodetic}}$ increases with $Q$ up to a threshold, beyond which it decreases. Panel (c) illustrates the transition from a black hole to a naked singularity as $Q$ exceeds the critical value, while panel (d) provides a three-dimensional visualisation of the overall behaviour across the spacetime geometry.