Distinguishing rotating Kiselev black hole from naked singularity using spin precession of test gyroscope

TL;DR

This paper proposes a method to distinguish rotating Kiselev black holes from naked singularities by analyzing the spin precession frequencies of test gyroscopes, providing a potential observational signature based on precession behavior.

Contribution

It introduces a novel approach using spin precession measurements to differentiate black holes from naked singularities in Kiselev spacetime, considering the effects of quintessential parameters.

Findings

Precession frequency diverges near black holes, indicating event horizons.

Precession remains finite for naked singularities, except at the singularity.

Lense-Thirring and geodetic precession frequencies are computed for these spacetimes.

Abstract

We study the critical values of the quintessential and spin parameters, to distinguish a rotating Kiselev black hole (RKBH) from a naked singularity. For any value of the dimensionless quintessential parameter $\omega_{q} \in (-1, -1/3)$, when increasing the value of quintessential parameter $\alpha$, the size of the event horizon increases, whereas the size of the outer horizon decreases. We then study the spin precession of a test gyroscope attached to a stationary observer in this spacetime. Using the spin precessions we differentiate black holes from naked singularities. If the precession frequency becomes large, as approaching to the central object in the quintessential field along any direction, then the spacetime is a black hole. A spacetime will contain a naked singularity if the precession frequency remains finite everywhere except at the singularity itself. Finally, we study the Lense-Thirring precession frequency for rotating Kiseleb black hole and the geodetic precession for Kiselev black hole.