Timelike symmetries and causality in Lorentzian manifolds

Abstract

Metric and curvature symmetries (Killing, homothetic, conformal, null convergence conditions...) of Riemannian, semi-Riemannian, and lightlike manifolds play an important role in theoretical physics, especially in general relativity. In the present paper, we investigate and discuss the consequences that spacetimes admit such symmetries and show that their existence places restrictions on both the null geometry of hypersurfaces and the different hierarchies of spacetime causality.