Total Magnification and Magnification Centroid Due to Strongly Naked Singularity Lensing

TL;DR

This paper analyzes gravitational lensing by a strongly naked singularity at the galactic center, calculating magnification properties and comparing them to black hole lenses, with implications for cosmic censorship hypotheses.

Contribution

It provides detailed calculations of magnification centroid, shift, and total magnification for SNS lensing using the Janis-Newman-Winicour metric, expanding previous work and highlighting observable differences from black holes.

Findings

Magnification centroid increases with source position.

Magnification centroid shift peaks then decreases with source position.

Total magnification decreases to one as source position grows.

Abstract

A strongly naked singularity (SNS) was modelled at the center of the Galaxy. This specific type of naked singularity was characterized in 2008 by Virbhadra and Keeton. The lens is described using the Janis-Newman-Winicour metric, which has an ordinary mass and massless scalar charge parameters. Gravitational lensing by the SNS gives rise to 4 images: 2 images on the same side as the source and 2 images on the opposite side of the source from the optic axis. We compute magnification centroid, magnification centroid shift, and total absolute magnification for many values of the angular source position. The nature of the curve for all three results are qualitatively similar to Schwarzschild black hole lenses, but quantitatively different. Magnification centroid increases as angular source position increases. As angular source position increases, magnification centroid shift increases to a maximum value, and then begins to decrease. As angular source position becomes large, magnification centroid shift will approach zero. Total magnification is large for small values of angular source position, and decreases to a limiting value of one. The results expand upon previous work on an SNS of {\nu}=0.01. If such observations were viewed experimentally, they would show support for an SNS at the galactic center. Interpretation of an SNS would disprove the cosmic censorship hypothesis by Penrose, as well as the weaker cosmic censorship hypothesis by Virbhadra, which allows the existence of weakly naked singularities.