Global Prescribed Mean Curvature foliations in cosmological spacetimes with matter, Part II

TL;DR

This paper investigates the global properties of Prescribed Mean Curvature foliations in cosmological spacetimes with matter, demonstrating the existence of such foliations under complex conditions involving local symmetries and Vlasov matter.

Contribution

It extends previous work by establishing the existence of global PMC foliations in more complex cosmological models with matter and symmetry, using advanced techniques.

Findings

Existence of global PMC foliations in spacetimes with local U(1) x U(1) symmetry.

Techniques more complex than in Part I are required for these proofs.

Spacetimes with Vlasov matter admit such foliations.

Abstract

This second part is devoted to the investigation of global properties of Prescribed Mean Curvature (PMC) foliations in cosmological spacetimes with local $U(1) \times U(1)$ symmetry and matter described by the Vlasov equation. It turns out, that these spacetimes admit a global foliation by PMC surfaces, as well, but the techniques to achieve this goal are more complex than in the cases considered in part I.