The plane symmetric Einstein-dust system with positive cosmological constant

TL;DR

This paper proves the global existence and analyzes the late-time behavior of solutions to the Einstein-dust system with positive cosmological constant under plane symmetry, contributing to understanding cosmological models with pressureless matter.

Contribution

It establishes the global classical solutions and investigates asymptotic properties for the Einstein-dust system with positive cosmological constant in plane symmetry, a novel result in this setting.

Findings

Global classical solutions exist under certain initial conditions.

Late-time asymptotic behavior of solutions is characterized.

Results enhance understanding of cosmological models with pressureless matter.

Abstract

The Einstein equations with a positive cosmological constant are coupled to the pressureless perfect fluid matter in plane symmetry. Under suitable restrictions on the initial data, the resulting Einstein-dust system is proved to have a global classical solution in the future time direction. Some late time asymptotic properties are obtained as well.