
TL;DR
This paper introduces and characterizes class A spacetimes, showing their equivalence to SCTP spacetimes, their topological properties, and their relevance to Lorentzian Aubry-Mather theory.
Contribution
It defines class A spacetimes, characterizes them as mapping tori, proves their equivalence to SCTP spacetimes, and explores their topological and geometric properties.
Findings
Class A spacetimes are characterized as mapping tori.
The set of class A spacetimes is open in the $C^0$-topology.
A coarse Lipschitz property for the time separation is established.
Abstract
We introduce class A spacetimes, i.e. compact vicious spacetimes such that the Abelian cover is globally hyperbolic. We study the main properties of class A spacetimes using methods similar to the one introduced in D. Sullivan "Cycles for the dynamical study of foliated manifolds and complex manifolds" (Invent. Math.,36, 225-255 (1976)) and D. Yu. Burago "Periodic metrics" (Representation theory and dynamical systems (Adv. Soviet 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 "Splitting theorems for spatially closed spacetimes" (Comm Math Phys 96:423-429, 1984). The set of class A spacetimes is shown to be open in the…
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
