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

Abstract

We consider here the precession of a test gyroscope in Kerr spacetimes to distinguish a naked singularity (NS) from black hole (BH). It is known that when the angular velocity of the gyro vanishes the spin precession frequency diverged at the ergo-surface. We show that it is possible to overcome this divergence by moving the gyro to the ergoregion with a non-zero angular velocity (\(\Omega_e\)) in a definite range. Then the frequency is finite and regular on the boundary of the ergoregion and inside, for both the BH and NS. Specifically, if we move the gyro with a non-zero \(\Omega_e\) to an unknown astrophysical object, its precession diverges on the event horizon for a black hole, but finite and regular for NS. Therefore a genuine detection for the existence or otherwise of the event horizon becomes possible. We also show that for a near-extremal (\(1<a_*<1.1\)) NS, some special features appear in precession frequency curves, using which a near-extremal NS can be distinguished from a BH, or NS with higher angular momentum. We then investigate the Lense-Thirring (LT) precession or nodal plane precession frequency, and other fundamental frequencies, for the accretion disk around a BH and NS to show that clear distinctions exist for BH and NS configurations in terms of radial variation features. The LT precession in equatorial circular orbits increases closer to BH, but for NS it increases, attains a peak and then decreases. Specifically, for \(a_*=1.089\), it decreases to reach \(0\) for certain \(r_{0}\), and acquires negative values for \(a_* > 1.089\). For \(1<a_*<1.089\), a peak appears, but vanishing or negative LT frequency are avoided. Hence there are important differences in accretion disk LT frequencies for BH and NS. As LT frequencies are intimately related to and can cause the observed QPOs, this may allow to determine whether a given astrophysical object is BH or NS.