# The effect of the Brane-Dicke coupling parameter on weak gravitational lensing by wormholes and naked singularities

## TL;DR

This study investigates how the Brane-Dicke coupling parameter influences weak gravitational lensing by wormholes and naked singularities using geometric and quantum-corrected methods, potentially aiding in their observational detection.

## Contribution

It introduces a novel analysis of the Brane-Dicke parameter's effect on lensing, incorporating quantum corrections and comparing wormholes with naked singularities.

## Key findings

- Brane-Dicke parameter significantly affects deflection angles.
- Quantum corrections modify classical lensing predictions.
- Distinct lensing signatures can help differentiate wormholes from naked singularities.

## Abstract

In this paper, we analyze the deflection angle of light by Brane-Dicke wormhole in the weak field limit approximation to find the effect of the Brane-Dicke coupling parameter on the weak gravitation lensing. For this purpose, we consider new geometric techniques, i.e., Gauss-Bonnet theorem and optical geometry in order to calculate the deflection angle. Furthermore, we verify our results by considering the most familiar geodesic technique. Moreover, we establish the quantum corrected metric of Brane-Dicke wormhole by replacing the classical geodesic with Bohmian trajectories, whose matter source and anisotropic pressure are influenced by Bohmian quantum effects and calculate its quantum corrected deflection angle. Then, we calculate the deflection angle by naked singularities and compare with the result of wormhole's. Such a novel lensing feature might serve as a way to detect wormholes, naked singularities and also the evidence of Brane-Dicke theory.