Causal Structure of Vacuum Solutions to Conformal(Weyl) Gravity

Abstract

Using Penrose diagrams the causal structure of the static spherically symmetric vacuum solution to conformal (Weyl) gravity is investigated. A striking aspect of the solution is an unexpected physical singularity at $r=0$ caused by a linear term in the metric. We explain how to calculate the deflection of light in coordinates where the metric is manifestly conformal to flat i.e. in coordinates where light moves in straight lines.Comment: 18 pages, 2 figures, title and abstract changed, contents essentially unaltered accepted for publication in General Relativity and Gravitatio