Strong gravitational lensing by a rotating non-Kerr compact object

TL;DR

This paper investigates how strong gravitational lensing behaves around a rotating non-Kerr compact object, revealing how deformation and rotation parameters influence photon trajectories and lensing observables.

Contribution

It introduces a model for rotating non-Kerr objects with deformation parameter and analyzes their lensing properties, highlighting differences from Kerr black holes and naked singularities.

Findings

Photon sphere radius depends sharply on deformation and rotation parameters.

Deflection angle behavior differs notably when the object is more prolate or oblate.

Numerical estimates for lensing observables around supermassive galactic objects are provided.

Abstract

We study the strong gravitational lensing in the background of a rotating non-Kerr compact object with a deformed parameter $\epsilon$ and an unbound rotation parameter $a$. We find that the photon sphere radius and the deflection angle depend sharply on the parameters $\epsilon$ and $a$. For the case in which the black hole is more prolate than a Kerr black hole, the photon sphere exists only in the regime $\epsilon\leq\epsilon_{max}$ for prograde photon. The upper limit $\epsilon_{max}$ is a function of the rotation parameter $a$. As $\epsilon>\epsilon_{max}$, the deflection angle of the light ray closing very to the naked singularity is a positive finite value, which is different from those in both the usual Kerr black hole spacetime and in the rotating naked singularity described by Janis-Newman-Winicour metric. For the oblate black hole and the retrograde photon, there does not exist such a threshold value. Modelling the supermassive central object of the Galaxy as a rotating non-Kerr compact object, we estimated the numerical values of the coefficients and observables for gravitational lensing in the strong field limit.