Time delay and magnification centroid due to gravitational lensing by black holes and naked singularities

TL;DR

This paper compares gravitational lensing effects, including time delay and magnification, caused by Schwarzschild black holes and Janis-Newman-Winicour naked singularities, revealing significant differences especially for strongly naked singularities.

Contribution

It provides a detailed analysis of lensing features for black holes and naked singularities, highlighting qualitative differences and the impact of scalar fields on lensing characteristics.

Findings

Lensing features are similar for black holes and weakly naked singularities.

Strongly naked singularities produce qualitatively different lensing effects.

Scalar fields decrease time delay and enhance magnification of images.

Abstract

We model the massive dark object at the center of the Galaxy as a Schwarzschild black hole as well as Janis-Newman-Winicour naked singularities, characterized by the mass and scalar charge parameters, and study gravitational lensing (particularly time delay, magnification centroid, and total magnification) by them. We find that the lensing features are qualitatively similar (though quantitatively different) for the Schwarzschild black holes, weakly naked, and marginally strongly naked singularities. However, the lensing characteristics of strongly naked singularities are qualitatively very different from those due the Schwarzschild black holes. The images produced by Schwarzschild black hole lenses and weakly naked and marginally strongly naked singularity lenses always have positive time delays. On the other hand, the strongly naked singularity lenses can give rise to images with positive, zero, or negative time delays. In particular, for a large angular source position the direct image (the outermost image on the same side as the source) due to strongly naked singularity lensing always has negative time delay. We also found that the scalar field decreases the time delay and increases the magnitude of magnifications of images; this result could have important implications for cosmology. As the Janis-Newman-Winicour metric also describes the exterior gravitational field of a scalar star, naked singularities as well as scalar star lenses, if these exist in nature, will serve as more efficient cosmic telescopes than regular gravitational lenses.