Gravitational radiation and isotropic change of the spatial geometry

To simplify a number of considerations in the weak field approximation, including the determination of the response of interferometric gravitational wave detectors, the "transverse traceless" (TT) gauge is often used. While the identification of the corresponding gauge invariant part of the metric perturbations in the pure vacuum case is obvious, it is not widely known that the determination and the use of the TT part is much more complicated and, in turn, much less rewarding when sources are involved. It is shown here that likewise the transverse part of the electric current in the Coulomb gauge within Maxwell's theory the sources of the TT gauge part of the metric perturbations become non-local. This, in practice, invokes the necessity of the use of more adequate projection operators then the ones applied, e.g, in the weak field limit, and in many post-Newtonian considerations. It is also pointed out that, whenever nonlinear effects are taken into account, some of the conclusions concerning the response of interferometric gravitational wave detectors may be influenced. In particular, attention is called on the possibility that gravitational radiation may produce an isotropic change of the spatial geometry.