# Gravitational Lensing in Weyl Gravity

## TL;DR

This paper calculates the light deflection angle in Weyl gravity, comparing it with Schwarzschild-de Sitter spacetime, and discusses discrepancies in the literature regarding these calculations.

## Contribution

It provides a detailed calculation of light deflection in Weyl gravity and analyzes reasons for conflicting results in previous studies.

## Key findings

- Deflection angle in Kottler spacetime includes cosmological constant effects
- Deflection in Mannheim-Kazanas spacetime accounts for additional parameters
- Identifies potential reasons for discrepancies in existing literature

## Abstract

We calculate the deflection angle of light from a distant source by a galaxy cluster in Weyl's conformal gravity. The general method of calculation is first applied to calculate the deflection angle in Schwarzschild-de Sitter (Kottler) spacetime. The deflection angle calculated in Kottler spacetime includes the contribution of the cosmological constant, which quantitatively agrees with one work and disagrees with many works in the literature. We then calculate the deflection angle in Mannheim-Kazanas spacetime in two conformally related coordinate systems and find that the result includes contributions from both the cosmological constant and the Mannheim-Kazanas parameter. There are conflicting results on the deflection angle for light in Weyl gravity in the literature. We point out a possible reason for the discrepancy between our work and the others.