Distinguishing Black Hole and Naked Singularity in MOG via Inertial Frame Dragging Effect

TL;DR

This paper investigates the inertial frame dragging effects around Kerr-MOG black holes and naked singularities, providing a method to distinguish these objects based on spin precession and epicyclic frequencies.

Contribution

It introduces a detailed analysis of generalized spin precession and frequency profiles in MOG gravity to differentiate black holes from naked singularities.

Findings

Generalized spin frequency depends on MOG parameters and distinguishes object types.

Lense-Thirring frequency diverges at the horizon for extremal black holes.

Epicyclic frequency profiles can identify non-extremal black holes, extremal black holes, and naked singularities.

Abstract

We analyze the generalized spin precession of a test gyroscope around a stationary spacetime i.e. for Kerr-MOG black hole~(BH) in scalar-tensor-vector gravity or modified gravity~(MOG). A detailed study of generalized spin frequency has been done for \emph{non} extremal Kerr-MOG BH, \emph{extremal} Kerr-MOG BH and \emph{naked singularity~(NS)} in comparison to non-extremal BH, extremal BH, and NS of Kerr spacetime. The generalized spin frequency that {we have} computed could be expressed in terms of {the} BH mass parameter, the angular momentum parameter, and the MOG parameter. Moreover, we differentiate the non-extremal BH, extremal BH, and NS via computation of the said precession frequency. The Lense-Thirring~(LT) frequency {can} obtain from generalized spin frequency by taking the limit as $\Omega=0$ i. e. {when the} angular frequency is set to zero limit. Furthermore, we compute the LT frequency for various {values of} angular coordinates i.e. starting from polar to {the} equatorial plane. We show that the LT frequency diverges at the horizon for extremal BH. Finally, we study the accretion disk physics by computing three epicyclic frequencies namely the Keplerian frequency, {the} radial epicyclic frequency and {the} vertical epicyclic frequency. We also compute the periastron frequency and nodal frequency. With the aid of these frequency profiles, {one} can distinguish three compact objects i. e. \emph{non-extremal BH, extremal BH} {and} \emph{NS}.