Exact gravitational lensing in conformal gravity and Schwarzschild-de Sitter spacetime

TL;DR

This paper derives an exact solution for gravitational lensing in conformal gravity and Schwarzschild-de Sitter spacetime, providing improved approximations and highlighting the impact of conformal gravity's parameters on light deflection.

Contribution

It presents an exact solution for light bending in these spacetimes and refines previous approximations by systematically excluding non-physical null trajectories.

Findings

Conformal gravity's parameter γ increases light deflection compared to General Relativity.

An improved small-angle approximation for lensing in these spacetimes.

Systematic exclusion of non-physical null trajectories in calculations.

Abstract

An exact solution is obtained for the gravitational bending of light in static, spherically symmetric metrics which includes the Schwarzschild-de Sitter spacetime and also the Mannheim-Kazanas metric of conformal Weyl gravity. From the exact solution, we obtain a small bending-angle-approximation for a lens system where the source, lens and observer are co-aligned. This expansion improves previous calculations where we systematically avoid parameter ranges that correspond to non-existent null trajectories. The linear coefficient $\gamma$ characteristic to conformal gravity is shown to contribute enhanced deflection compared to the angle predicted by General Relativity for small $\gamma$.