# On gravitational lensing by symmetric and asymmetric wormholes

## TL;DR

This paper explores how gravitational lensing behaves in symmetric and asymmetric wormholes, highlighting the role of photon spheres and analyzing specific wormhole models with detailed deflection angle calculations.

## Contribution

It provides a detailed analysis of gravitational lensing in asymmetric wormholes, including photon sphere behavior and deflection angles for specific wormhole solutions.

## Key findings

- Photon spheres exist in all wormholes, influencing lensing behavior.
- Asymmetric wormholes can allow photons to cross the throat and return.
- Deflection angles vary significantly depending on wormhole symmetry and configuration.

## Abstract

We discuss the peculiarities of gravitational lensing by spherically symmetric wormholes if they are not symmetric with respect to their throats. It is noticed, in particular, that wormholes always contain the so-called photon spheres, near which the photon deflection angles can be arbitrarily large, but, in general, the throat is such a sphere only for symmetric wormholes. In some cases, photons from outside can cross the throat and return back from a neighborhood of a photon sphere if the latter is located beyond the throat. Two families of generally asymmetric wormhole configurations are considered as examples: (1) anti-Fisher wormholes with a massless phantom scalar field as a source of gravity, and (2) wormholes with a zero Ricci scalar that may be interpreted as vacuum configurations in a brane world. For these metrics, the photon effective potentials and deflection angles are found and discussed.