Abstract. We introduce class A spacetimes, i.e. compact vicious spacetimes (M; g) such that the Abelian cover (M; g) is globally hyperbolic. We study the main properties of class A spacetimes using methods similar to the one introduced in [19] and [3]. As a consequence we are able to characterize manifolds admitting class A metrics completely as mapping tori. The set of class A spacetimes is shown to be open in the C0-topology on the set of Lorentzian metrics. As an application we prove a coarse Lipschitz property for the time
separation of the Abelian cover.