Zusammenfassung
We introduce class A spacetimes, i.e. compact vicious spacetimes (M, g) such that the Abelian cover is globally hyperbolic. We study the main properties of class A spacetimes using methods similar to those introduced in Sullivan (Invent Math 36:225-255, 1976) and Burago (Adv Sov Math 9:205-210, 1992). As a consequence we are able to characterize manifolds admitting class A metrics completely as ...
Zusammenfassung
We introduce class A spacetimes, i.e. compact vicious spacetimes (M, g) such that the Abelian cover is globally hyperbolic. We study the main properties of class A spacetimes using methods similar to those introduced in Sullivan (Invent Math 36:225-255, 1976) and Burago (Adv Sov Math 9:205-210, 1992). As a consequence we are able to characterize manifolds admitting class A metrics completely as mapping tori. Further we show that the notion of class A spacetime is equivalent to that of SCTP (spacially compact time-periodic) spacetimes as introduced in Galloway (Comm Math Phys 96:423-429, 1984). The set of class A spacetimes is shown to be open in the C (0)-topology on the set of Lorentzian metrics. As an application we prove a coarse Lipschitz property for the time separation of the Abelian cover. This coarse Lipschitz property is an essential part in the study of Aubry-Mather theory in Lorentzian geometry.
Altmetric