Gravitational Lensing by Rotating Naked Singularities

TL;DR

This paper analyzes gravitational lensing effects caused by rotating naked singularities modeled within Einstein-massless scalar field theory, revealing how scalar charge influences image positions, magnifications, and critical curves in both weak and strong deflection regimes.

Contribution

It provides analytical and numerical insights into lensing by naked singularities, highlighting the impact of scalar charge and angular momentum on observable lensing features.

Findings

Scalar charge affects the shift of critical curves.

Naked singularities cause drift of caustics away from the optical axis.

Relativistic images' positions and separability are computed for weakly naked singularities.

Abstract

We model massive compact objects in galactic nuclei as stationary, axially-symmetric naked singularities in the Einstein-massless scalar field theory and study the resulting gravitational lensing. In the weak deflection limit we study analytically the position of the two weak field images, the corresponding signed and absolute magnifications as well as the centroid up to post-Newtonian order. We show that there are a static post-Newtonian corrections to the signed magnification and their sum as well as to the critical curves, which are function of the scalar charge. The shift of the critical curves as a function of the lens angular momentum is found, and it is shown that they decrease slightingly for the weakly naked and vastly for the strongly naked singularities with the increase of the scalar charge. The point-like caustics drift away from the optical axis and do not depend on the scalar charge. In the strong deflection limit approximation we compute numerically the position of the relativistic images and their separability for weakly naked singularities. All of the lensing quantities are compared to particular cases as Schwarzschild and Kerr black holes as well as Janis--Newman--Winicour naked singularities.