Spin precession in a black hole and naked singularity spacetimes

TL;DR

This paper introduces a criterion based on gyroscopic spin precession to distinguish Kerr naked singularities from black holes, revealing distinct behaviors in precession frequencies related to the ergoregion geometry.

Contribution

It proposes a novel method using spin precession behavior to differentiate black holes from naked singularities based on their ergoregion geometry.

Findings

Precession frequency diverges near black hole horizons.

Precession frequency remains finite for naked singularities.

Lense-Thirring precession decreases with radius in naked singularities.

Abstract

We propose here a specific criterion to address the existence or otherwise of Kerr naked singularities, in terms of the precession of the spin of a test gyroscope due to the frame dragging by the central spinning body. We show that there is indeed an important characteristic difference in the behavior of gyro spin precession frequency in the limit of approach to these compact objects, and this can be used, in principle, to differentiate the naked singularity from black hole. Specifically, if gyroscopes are fixed all along the polar axis upto 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. Interestingly, this behavior is intimately related to and is governed by the geometry of the ergoregion in each of these cases which we analyze here. One intriguing behavior that emerges is, in the Kerr naked singularity case, the Lense-Thirring precession frequency ($\Omega_{\rm LT}$) of the gyroscope due to frame-dragging effect decreases as ($\Omega_{\rm LT}\propto r$) after reaching a maximum, in the limit of $r= 0$, as opposed to $r^{-3}$ dependence in all other known astrophysical cases.