This is an important and natural question as the spacetime shear, inhomogeneity and tidal effects are all intertwined via the Einstein field equations. Though many solutions with these properties exist in the literature, in this paper we identify, via a geometrical analysis, the important physical reason behind these solutions. We show that such scenarios are possible for limited classes of equations of state that are solutions to a highly nonlinear and fourth order differential equation. To show this, we use a covariant semitetrad spacetime decomposition and present a novel geometrical classification of shear-free Locally Rotationally Symmetric (LRS-II) perfect fluid self-gravitating systems, in terms of the covariantly defined fluid acceleration and the fluid expansion. Noteworthily, we deduce the governing differential equation that gives the possible limited equations of state of matter.

We numerically investigate the propagation of plane gravitational waves in the form of an initial boundary value problem with de Sitter initial data. The full non-linear Einstein equations with positive cosmological constant λ are written in the Friedrich-Nagy gauge which yields a wellposed system. The propagation of a single wave and the collision of two with colinear polarization are studied and contrasted with their Minkowskian analogues. Unlike with λ = 0, critical behaviours are found with λ > 0 and are based on the relationship between the wave profile and λ. We find that choosing boundary data close to one of these bifurcations results in a "false" steady state which violates the constraints. Simulations containing (approximate) impulsive wave profiles are run and general features are discussed. Analytic results of Woodard and Tsamis [1, 2], which describe how gravitational waves could affect an expansion rate at an initial instance of time, are explored and generalized to the entire spacetime. Finally we put forward boundary conditions that, at least locally, slow down the expansion considerably for a time.

We numerically investigate the propagation of plane gravitational waves in the form of an initial boundary value problem with de Sitter initial data. The full non-linear Einstein equations with positive cosmological constant λ are written in the Friedrich–Nagy gauge which yields a wellposed system. The propagation of a single wave and the collision of two with colinear polarization are studied and contrasted with their Minkowskian analogues. Unlike with λ=0, critical behaviours are found with λ>0 and are based on the relationship between the wave profile and λ. We find that choosing boundary data close to one of these bifurcations results in a “false” steady state which violates the constraints. Simulations containing (approximate) impulsive wave profiles are run and general features are discussed. Analytic results of Tsamis and Woodard, which describe how gravitational waves could affect an expansion rate at an initial instance of time, are explored and generalized to the entire space–time. Finally we put forward boundary conditions that, at least locally, slow down the expansion considerably for a time.