Some high-frequency gravitational waves related to exact radiative spacetimes

TL;DR

This paper introduces a formalism for high-frequency gravitational waves applicable to various spacetimes, generalizes existing methods, and presents explicit solutions in different cosmological backgrounds.

Contribution

It extends the Isaacson high-frequency approximation to non-vacuum spacetimes and provides explicit solutions for different wave types in diverse backgrounds.

Findings

Developed a unified formalism for gravitational waves in various spacetimes.

Generalized Isaacson's method to include non-vacuum backgrounds.

Presented explicit solutions for high-frequency waves in multiple cosmological models.

Abstract

A formalism is introduced which may describe both standard linearized waves and gravitational waves in Isaacson's high-frequency limit. After emphasizing main differences between the two approximation techniques we generalize the Isaacson method to non-vacuum spacetimes. Then we present three large explicit classes of solutions for high-frequency gravitational waves in particular backgrounds. These involve non-expanding (plane, spherical or hyperboloidal), cylindrical, and expanding (spherical) waves propagating in various universes which may contain a cosmological constant and electromagnetic field. Relations of high-frequency gravitational perturbations of these types to corresponding exact radiative spacetimes are described.