Gravitational wave propagation in isotropic cosmologies

Abstract

We study the propagation of gravitational waves carrying arbitrary information through isotropic cosmologies. The waves are modelled as small perturbations of the background Robertson-Walker geometry. The perfect fluid matter distribution of the isotropic background is, in general, modified by small anisotropic stresses. For pure gravity waves, in which the perturbed Weyl tensor is radiative (i.e. type N in the Petrov classification), we construct explicit examples for which the presence of the anisotropic stress is shown to be essential and the histories of the wave-fronts in the background Robertson-Walker geometry are shear-free null hypersurfaces. The examples derived in this case are analogous to the Bateman waves of electromagnetic theory.

Some Gravity Waves in Isotropic Cosmologies

“…The equations satisfied by these variables are obtained from the Ricci identities, the Bianchi identities and, for the consistency of the field equations and the Bianchi identities, the vanishing covariant divergence of the matter energy-momentum-stress tensor. Working in the context of this latter approach, perturbations describing gravitational waves have been obtained by looking for gauge invariant variables having an arbitrary dependence on a scalar function [5,6]. This was an implementation of Trautman's [7] characterization of waves, namely, that waves can propagate information with the information encoded in the arbitrary scalar function.…”

Editorial note to: Manfred Trümper, A threedimensional formulation of the Bianchi identities for vacuum gravitational fields

“…in [23], and they appear in chapter 1, section 5, of [14]. The results (equations ( 9)- (12) of the paper) are stated for the vacuum case but it is relatively straightforward to add the Ricci tensor terms.…”

“…The work soon became known to the group in Cambridge led by Dennis Sciama, through the report and a seminar there by Trümper. This led to the first appearance of equations ( 9)- (12) in a refereed journal in [9], where they were extended to include a perfect fluid Ricci tensor, though [31] had earlier given them as specialized to the pure electric case. 1 The equations with a general Ricci tensor, written in terms of the energy-momentum of a generic imperfect fluid, are given in the appendix to [8].…”

“…[24]) and to improve understanding of gravitational waves ( [25]), though there is no analogue in the gravitational case of the constitutive equations or of magnetic permeability and dielectric constant. The equations (11) and (12), with the Ricci tensor terms added, are like the Maxwell equations commonly written as ∇ E = j and ∇ H = 0. A series of papers by Hogan and colleagues ( [10][11][12]) established interesting results relating electromagnetic and gravitational perturbations of Robertson-Walker cosmologies, [11] being particularly interesting as it shows how gravitational waves in cosmology can generate electromagnetic waves from a test magnetic field.…”

“…They are given in[20] and in the source-free case, using a differential form notation, in[13]. A general form similar to (9)-(12) appears in[21].…”