Aubry-Mather theory and Lipschitz continuity of the time separation

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 A₁, we obtain improved results on timelike maximizers and Lipschitz continuity of the time separation of the Abelian cover on the i. g. optimal subsets.