Distinguishing Signature of Kerr-MOG Black Hole and Superspinar via Lense-Thirring Precession

TL;DR

This paper compares the Lense-Thirring precession signatures of Kerr-MOG black holes and superspinars, revealing distinct geometrical and dynamical features that could help differentiate these objects observationally.

Contribution

It introduces a detailed analysis of Lense-Thirring precession in Kerr-MOG spacetimes, highlighting differences between black holes and superspinars not previously characterized.

Findings

LT precession frequency along the pole is proportional to spin and inversely proportional to radial distance cubed.

In superspinars, LT precession decreases with distance and is inversely proportional to the cube of the spin parameter.

Distinct angular dependence of LT precession frequency can differentiate black holes from superspinars.

Abstract

We examine the geometrical differences between the black hole~(BH) and naked singularity~(NS) or superspinar via Lense-Thirring~(LT) precession in spinning modified-gravity~(MOG). For BH case, we show that the LT precession frequency~($\Omega_{LT}$) along the pole is proportional to the angular-momentum~($J$) parameter or spin parameter~($a$) and is inversely proportional to the cubic value of radial distance parameter, and also governed by Eq.(1). Along the equatorial plane it is governed by Eq.(2). While for superspinar, we show that the LT precession frequency is inversely proportional to the cubic value of the spin parameter and it decreases with distance by MOG parameter as derived in Eq.(3) at the pole and in the limit $a>>r$ (where $\alpha$ is MOG parameter). For $\theta\neq\frac{\pi}{2}$ and in the superspinar limit, the spin frequency varies as $\Omega_{LT}\propto \frac{1}{a^3\cos^4\theta}$ and by Eq.(38)