Plane-symmetric spacetimes with positive cosmological constant. The case of stiff fluids

Abstract

We consider plane-symmetric spacetimes satisfying Einstein's field equations with positive cosmological constant, when the matter is a fluid whose pressure is equal to its mass-energy density (i.e. a so-called stiff fluid). We study the initial-value problem for the associated Einstein equations and establish a global existence result. The late-time asymptotics of solutions is also rigorously derived, and we conclude that the spacetime approaches the de Sitter spacetime while the matter disperses asymptotically. A technical difficulty dealt with here lies in the fact that solutions may contain vacuum states as well as velocities approaching the speed of light, both possibilities leading to singular behavior in the evolution equations.