A Morse-theoretical analysis of lensing in wormhole spacetimes

TL;DR

This paper uses Morse theory to analyze gravitational lensing in certain stationary, axisymmetric wormhole spacetimes, demonstrating that observers see infinitely many images of a light source under mild conditions.

Contribution

It introduces a Morse-theoretical framework to study lensing in wormholes and proves the existence of infinitely many images for generic observer-source configurations.

Findings

Observers see infinitely many images of a light source.

Morse theory provides a rigorous method for analyzing lensing.

Qualitative features of lightlike geodesics are characterized using potentials.

Abstract

We consider a class of stationary and axisymmetric wormhole spacetimes that is closely related to, but not identical with, the class of Teo wormholes. We fix a point $p$ (observation event) and a timelike curve $\gamma$ (worldline of a light source), and we characterize the set of all past-oriented lightlike geodesics from $p$ to $\gamma$. As any such geodesic corresponds to an image of the light source on the observer's sky, this allows us to investigate the lensing properties of the wormhole. As a main result, we prove with the help of Morse theory that, under very mild conditions on $\gamma$, the observer always sees infinitely many images of $\gamma$. Moreover, we study some qualitative features of the lightlike geodesics with the help of two potentials that determine the sum of centrifugal and Coriolis forces of observers in circular motion for the case that the observers' velocity approaches the velocity of light. We exemplify the general results with two specific wormhole spacetimes.