Throat effects on strong gravitational lensing in Kerr-like wormholes

TL;DR

This paper investigates strong gravitational lensing by Kerr-like wormholes, revealing unique divergence behaviors of light deflection near the throat and discussing potential observational signatures distinguishing wormholes from black holes.

Contribution

It introduces a detailed analysis of lensing in Kerr-like wormholes, including divergence types and effective potential construction, highlighting features that could identify wormholes observationally.

Findings

Logarithmic divergence of deflection angle near double roots.

Stronger power-law divergence occurs near triple roots.

Effective potential analysis shows possible light paths through the wormhole.

Abstract

We study strong gravitational lensing by a specific one-parameter extension of Kerr spacetime, a Kerr-like wormhole, characterized by a single parameter specifying the throat's location. We classify the roots of the radial potential derived from the null geodesic equations. We focus on the conditions required for the throat, together with the other roots, to become either a double root or a triple root, potentially leading to the divergence of the deflection angle of the light rays in the strong deflection limit (SDL). In particular, while a logarithmic divergence of the deflection angle is known to occur as the closest distance $r_0$ of an incident light trajectory around a black hole approaches a double root, a stronger power-law (nonlogarithmic) divergence is found as $r_0$ approaches a triple root especially in a wormhole. In addition, the effective potential in terms of the proper distance from the throat is constructed, with which one can see how the light rays can either travel within a single spacetime, where both the source and the observers are located, or pass from the source through the throat into another spacetime where different observers reside. Observational effects, such as relativistic images resulting from the deflection of light by wormholes, are discussed, and they could serve as a unique feature of wormholes.