Strong gravitational lensing by a strongly naked null singularity

TL;DR

This paper investigates the unique strong gravitational lensing effects caused by a naked null singularity lacking a photon sphere, revealing distinctive divergence behavior and resolvable relativistic rings.

Contribution

It provides the first analysis of strong lensing features of a naked singularity without a photon sphere, including an analytic formula for nonlogarithmic divergence.

Findings

Bending angle diverges nonlogarithmically near the singularity.

Relativistic rings are well separated and potentially observable.

Distinct lensing signatures differentiate naked singularities from black holes.

Abstract

We study strong gravitational lensing in a static, spherically symmetric, naked singularity spacetime, without a photon sphere. The nature of the singularity is found to be lightlike. We discuss the characteristic lensing features of this naked singularity in the strong deflection limit. In spite of the absence of a photon sphere in this spacetime, the bending angle of light diverges, as it approaches the singularity. However, unlike black holes, it is found that the nature of this divergence is nonlogarithmic, and we derive an analytic formula for the same. Moreover, the relativistic rings produced due to strong lensing by the singularity are found to be well separated from each other, making them easy to resolve and possibly detect. These features are expected to be important in the study of strong lensing by ultracompact objects, especially ones without event horizons.