# Gravitational lensing by scalar-tensor wormholes and the energy conditions

## TL;DR

This paper investigates gravitational lensing effects of scalar-tensor wormholes, linking lensing features to energy conditions, and explores the implications for detecting such wormholes through Einstein rings.

## Contribution

It introduces a new concept of a zero deflection surface related to energy condition violations in wormholes within scalar-tensor gravity.

## Key findings

- Positive deflection occurs with nonexotic matter.
- Negative or zero deflection possible with exotic matter.
- Existence of a zero deflection surface linked to energy condition violations.

## Abstract

We study gravitational lensing by a class of zero Ricci scalar wormholes which arise as solutions in a scalar-tensor theory of gravity. An attempt is made to find a possible link between lensing features, stable/unstable photon orbits and the energy conditions on the matter required to support these spacetimes. Our analysis shows (for this class of wormholes) that light rays always exhibit a positive deflection if the energy conditions are satisfied (nonexotic matter content). In contrast, if the energy conditions are violated (exotic matter), the net deflection of a light ray may be positive, negative or even zero, depending on values of the metric and impact parameters. This prompts us to introduce a surface defined by a turning point value at which the net deflection of a light ray is equal to zero, even though we have a curved spacetime geometry. We argue that the existence of such a surface may be linked to exotic/energy condition violating matter. Wormholes in modified gravity with matter satisfying the energy conditions do not seem to have such a zero deflection surface. Finally, we study strong gravitational lensing briefly and also look into the formation of Einstein and relativistic Einstein rings. We conclude with some estimates on the wormhole mass, throat-radius and the detectability of the Einstein rings.