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

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 ($1 1.089$ 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.