Plane waves in a relativistic homogeneous and isotropic elastic continuum

TL;DR

This paper investigates the behavior of gravitational and acoustic plane waves in a relativistic, homogeneous, isotropic elastic medium within a flat universe, deriving equations governing wave amplitudes and analyzing specific cases like stiff ultrarigid continua.

Contribution

It develops a relativistic theory of plane wave propagation in elastic continua, extending nonrelativistic concepts to a general relativistic context.

Findings

Derived differential equations for wave amplitude evolution.

Described longitudinal acoustic waves with coupled first-order equations.

Analyzed plane waves in a stiff ultrarigid continuum.

Abstract

Propagation of gravitational and acoustic plane waves in a flat universe filled with a general relativistic, homogeneous and isotropic, spatially flat continuum is studied. The continuum is described by analogues of nonrelativistic characteristics, namely energy per particle, pressure and Lame coefficients, and considered in the comoving proper-time gauge. For all modes with the given wave covector, differential equations governing the time dependence of the amplitudes are derived. In particular, longitudinal acoustic waves are described, in analogy with the nonrelativistic theory, by two coupled first-order equations. As an example, plane waves in a stiff ultrarigid continuum are considered.