Some High-Frequency Gravitational Waves Related to Exact Radiative Spacetimes

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.

Kundt spacetimes minimally coupled to scalar field

“…(16). With this form of the metric function H (50), we obtain two independent Einstein equations with a nontrivial right-hand side (all other equations are already satisfied).…”

“…More general solutions possibly containing additional pure radiation and (exact) gravitational waves were found as well (for a review see, e.g., [15]). The pure radiation solutions can be used to support perturbative gravitational waves as well [16].…”

Evolution of high-frequency gravitational waves in some cosmological models

“…for the perturbations h µν on the curved background γ µν (considering the vacuum complete metric g µν or the case of a stress-energy tensor which does not contain derivatives of the metric, as shown in [13]). The two terms of the next order O(1), namely R…”

“…µν , can be used to provide the equation for the background (nonvacuum) metric [11,13] which involves the essential influence of the high-frequency gravitational waves on the background. Of course, to obtain a consistent solution, one has to solve both the wave equation and the equation for the background simultaneously.…”

“…The complete Isaacson's formalism thus consistently combines the equation for high-frequency waves with the equation describing back-reaction of the waves on the background. Recently we investigated this effect using the WKB form of the gravitational-wave perturbations [13] and we presented relations between these solutions and some exact radiative cosmological models.…”