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 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 $\gamma$.

22 pages, 8 figures

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• Test of conformal theory of gravity as an alternative paradigm to dark matter hypothesis from gravitational lensing studies
• Deflection and gravitational lensing of null and timelike signals in general asymptotically (anti-)de Sitter spacetimes
• Statistical Strong Lensing as a Test of Conformal Gravity