Distinguishing Kerr naked singularities and black holes using the spin precession of a test gyro in strong gravitational fields

TL;DR

This paper investigates how the spin precession of a test gyroscope and Lense-Thirring precession in accretion disks can be used to distinguish Kerr naked singularities from black holes, providing potential observational signatures.

Contribution

It introduces new methods to differentiate Kerr naked singularities from black holes by analyzing spin precession frequencies and accretion disk properties.

Findings

Precession frequencies are finite and regular for NS, diverging only at the singularity.

Distinct radial profiles of LT precession frequencies differentiate BHs from NS.

LT precession features relate to observed QPOs, aiding in identifying the nature of compact objects.

Abstract

We study here the precession of the spin of a test gyroscope attached to a stationary observer in the Kerr spacetime, specifically, to distinguish naked singularity (NS) from black hole (BH). It was shown recently that for gyros attached to static observers, their precession frequency became arbitrarily large in the limit of approach to the ergosurface. For gyros attached to stationary observers that move with non-zero angular velocity $\Omega$, this divergence at the ergosurface can be avoided. Specifically, for such gyros, the precession frequencies diverge on the event horizon of a BH, but are finite and regular for NS everywhere except at the singularity itself. Therefore a genuine detection of the event horizon becomes possible in this case. We also show that for a near-extremal NS ($1<a_* < 1.1$), characteristic features appear in the radial profiles of the precession frequency, using which we can further distinguish a near-extremal NS from a BH, or even from NS with larger angular momentum. We then investigate the Lense-Thirring (LT) precession or nodal plane precession frequency of the accretion disk around a BH and NS to show that clear distinctions exist for these configurations in terms of radial variation features. The LT precession in equatorial circular orbits increases with approach to a BH, whereas for NS it increases, attains a peak and then decreases. Interestingly, for $a_*=1.089$, it decreases until it vanishes at a certain radius, and acquires negative values for $a_* > 1.089$ for a certain range of $r$. For $1<a_*<1.089$, a peak appears, but the LT frequency remains positive definite. There are important differences in accretion disk LT frequencies for BH and NS and since LT frequencies are intimately related to observed QPOs, these features might allow us to determine whether a given rotating compact astrophysical object is BH or NS.