Causal Properties of Fibered Space-Time

On the space of a principal bundle, a Lorentzian metric and a time orientation are given that are invariant with respect to the action of the structure group. These objects form a fibered space-time and, in the case of spacelike fibers, induce the same structures on the base. The following causality conditions are discussed: chronology, causality, stable and strong causality, and global hyperbolicity. It is proved that if the base space-time satisfies one of the above conditions, then so does the fibered space-time.