Gravitational waves propagating into Friedmann--Robertson--Walker universes

TL;DR

This paper analyzes gravitational waves propagating into Friedmann-Robertson-Walker universes, detailing wavefront geometries, exact solutions, and the effects of wave interactions and backscattering.

Contribution

It provides a comprehensive analysis of gravitational wavefront geometries and exact solutions in FRW universes, including wave interactions and backscattering effects.

Findings

Wavefronts can be planar, cylindrical, or toroidal depending on universe type.

Exact solutions describe gravitational waves with stiff fluid equations of state.

Waves may include impulsive, step, or shock components and are generally backscattered.

Abstract

We consider space-times with two isometries which represent gravitational waves with distinct wavefronts which propagate into exact Friedmann-Robertson-Walker (FRW) universes. The geometry of possible wavefronts is analysed in detail in all three types of FRW models. In the spatially flat and open universes, the wavefronts can be planar or cylindrical; in the closed case they are toroidal. Exact solutions are given which describe gravitational waves propagating into the FRW universes with a fluid with a stiff equation of state. It is shown that the plane-fronted waves may include impulsive or step (shock) components, while the cylindrical waves in the spatially flat and open universes and the toroidal waves in closed universes may contain steps. In general, wavefronts may exist which have an arbitrary finite degree of smoothness. In all cases, the waves are backscattered. The head-on collision of such waves is also briefly mentioned.