Homogeneous plane-wave spacetimes and their stability

Homogeneous Plane-wave Spacetimes and their Stability

We consider the stability of spatially homogeneous plane-wave spacetimes. We carry out a full analysis for plane-wave spacetimes in (4 + 1) dimensions, and find there are two cases to consider; what we call nonexceptional and exceptional. In the non-exceptional case the plane waves are stable to (spatially homogeneous) vacuum perturbations as well as a restricted set of matter perturbations. In...

Asymptotically Plane Wave Spacetimes and their Actions

We propose a definition of asymptotically plane wave spacetimes in vacuum gravity in terms of the asymptotic falloff of the metric, and discuss the relation to previously constructed exact solutions. We construct a well-behaved action principle for such spacetimes, using the formalism developed by Mann and Marolf. We show that this action is finite on-shell and that the variational principle is...

Inhomogeneous Perturbations of Plane-wave Spacetimes

Recently it was shown that the exact cosmological solutions known as the vacuum plane-wave solutions are late-time attractors for an open set of the spatially homogeneous Bianchi universes containing a non-inflationary γ-law perfect fluid. In this paper we study inhomogeneous perturbations of these plane-wave spacetimes. By using expansion-normalised scale-invariant variables we show that these...

Compressible viscoelasticity: stability of solutions for homogeneous plane-Earth models

ShockWaves in Plane Symmetric Spacetimes

We consider Einstein’s equations coupled to the Euler equations in plane symmetry, with compact spatial slices and constant mean curvature time. We show that for a wide variety of equations of state and a large class of initial data, classical solutions break down in finite time. The key mathematical result is a new theorem on the breakdown of solutions of systems of balance laws. We also show ...