Causality violating paths are known to exist in many spacetimes satisfying the Einstein field equations, especially those solutions associated with rotating matter or rotating singularities [1–3] (see also Bonnor [4], and references in [5]). However, examples of causality violating geodesics are sparse in the scientific literature. Chandrasekhar and Wright [6] showed that the Gödel spacetime [1...

Conformal gravity has been proposed as an alternative theory of gravity which can account for flat galactic rotation curves without recourse to copious quantities of dark matter. However it was shown that for the usual choice of the metric, the result is catastrophic for null or highly relativistic geodesics, the effect is exactly the opposite yielding an effective repulsion and less deflection...

We associate certain probability measures on R to geodesics in the space HL of positively curved metrics on a line bundle L, and to geodesics in the finite dimensional symmetric space of hermitian norms on H(X, kL). We prove that the measures associated to the finite dimensional spaces converge weakly to the measures related to geodesics in HL as k goes to infinity. The convergence of second or...