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

Understand

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.