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

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 coaligned. This expansion improves previous calculations where we systematically avoid parameter ranges that correspond to nonexistent null trajectories. The linear coefficient $\ensuremath{\gamma}$ characteristic to conformal gravity is shown to contribute enhanced deflection compared to the angle predicted by general relativity for small $\ensuremath{\gamma}$.