Chaotic shadow of a non-Kerr rotating compact object with quadrupole mass moment

TL;DR

This paper numerically analyzes the shadows of non-Kerr rotating compact objects with quadrupole moments, revealing how deviations from Kerr metrics affect shadow shape, structure, and observable features like Einstein rings.

Contribution

It introduces a detailed numerical study of shadows for non-Kerr objects with quadrupole moments, highlighting effects of quadrupole deviations on shadow morphology and observable phenomena.

Findings

Shadow shape varies with quadrupole deviation: prolate for negative, oblate for positive.

Disorder regions and broken Einstein rings appear at certain deviation thresholds.

Concentric bright rings are observable along the rotation axis for specific observer directions.

Abstract

We have studied numerically the shadows of a non-Kerr rotating compact object with quadrupole mass moment, which belongs to Manko-Novikov family. The non-integrable photon motion caused by quadrupole mass moment affects sharply the shadow of the compact object. As the deviation parameter related to quadrupole mass moment is negative, the shadow of compact object is prolate and there are two disconnected main shadows with eyebrows located symmetrically on both sides of the equatorial plane. As the deviation parameter is positive, the shadow becomes oblate and the main shadow is joined together in the equatorial plane. Moreover, in this positive cases, there is a disorder region in the left of shadow which increases with the quadrupole-deviation parameter. Interestingly, we also find that Einstein ring is broken as the deviation from Kerr metric is larger than a certain critical value. This critical value decreases with the rotation parameter of black hole. Especially, the observer on the direction of rotation axis will find some concentric bright rings in the black disc. Finally, supposing that the gravitational field of the supermassive central object of the galaxy described by this metric, we estimated the numerical values of the observables for the black hole shadow.