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

We study here the precession of the spin of a test gyroscope attached to a stationary observer in the Kerr spacetime, specifically, to distinguish a naked singularity (NS) from a 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 nonzero angular velocity Ω, 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 a 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 a 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 on approaching 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 it 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 a BH and a NS and since LT frequencies are intimately related to observed quasiperiodic oscillations, these features might allow us to determine whether a given rotating compact astrophysical object is a BH or a NS.