A Morsetheoretical analysis of lensing in wormhole spacetimes
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 pastoriented 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.
 Publication:

arXiv eprints
 Pub Date:
 September 2021
 arXiv:
 arXiv:2109.12681
 Bibcode:
 2021arXiv210912681H
 Keywords:

 General Relativity and Quantum Cosmology;
 Mathematical Physics