Aubry-Mather theory and Lipschitz continuity of the time separation

TL;DR

This paper explores Aubry-Mather theory within a specific class of spacetimes, establishing improved results on timelike maximizers and demonstrating Lipschitz continuity of the time separation function on certain optimal subsets.

Contribution

It introduces the class A_1 of spacetimes and provides enhanced results on timelike maximizers and the Lipschitz continuity of the time separation in this setting.

Findings

Improved understanding of timelike maximizers in class A_1 spacetimes.

Proved Lipschitz continuity of the time separation function on optimal subsets.

Extended Aubry-Mather theory to a new subclass of spacetimes.

Abstract

We consider Aubry-Mather theory for a subclass of class A spacetimes, i.e. compact vicious spacetimes with globally hyperbolic Abelian cover. In this subclass, called class A_1, we obtain improved results on timelike maximizers and Lipschitz continuity of the time separation of the Abelian cover on the i.g. optimal subsets.