Abstract
This paper first presents a fully covariant formulation of Maxwell's equations in matter in the general relativistic framework. Although covariant, this formulation uses only essentially spatial four-vector fields and places in evidence the kinematical couplings (vorticity) and inertial effects (curvature of worldlines) which appear in Maxwell's equations for matter. Using a scaling of these equations enables one to construct covariant “quasi-electrostatic” and “quasi-magnetostatic” approximations. Theformer is used to establish the equations that govern piezoelectric gravitational-wave detectors. Furthermore, if a pyroelectric crystal is used in this type of device, then Gauss' law is shown to be modified and contains a contribution due to the incident gravitational perturbation.
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