Gravitational and acoustic waves in an elastic medium

Abstract

Relativistic equations governing perturbations of an elastic medium under the influence of gravitational waves are derived firstly in a gauge-independent way in terms of relative strains, and secondly in terms of gauge-dependent displacements. The derivations are based on the exact nonlinear theory of elasticity in conjunction with Einstein's theory of gravity, and hence are applicable to the solid crusts and cores of neutron stars. It is shown that in the approximately Minkowskian weak-field limit the equations reduce to those derived by previous workers for application in terrestrial contexts such as the detection of gravitational waves by a Weber bar.