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I shall discuss 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). If gyroscopes are fixed all along the polar axis up to the horizon of a Kerr black hole, the precession frequency becomes arbitrarily high, blowing up as the event horizon is approached. On the other hand, in the case of naked singularity, this frequency remains always finite and well behaved. One intriguing behavior that emerges is, in the Kerr naked singularity case, the Lense-Thirring (LT) precession frequency (ΩLT) of the gyroscope due to frame-dragging effect decreases as (ΩLT∝r) after reaching a maximum, in the limit of r ---> 0, as opposed to r−3 dependence in all other known astrophysical cases. For gyros attached to stationary observers that move with nonzero angular velocity Ω, 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. I shall then discuss the LT precession or nodal plane precession 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. 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.
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