Comparison of metrics from retarded integrals and transverse traceless subgauge

The time-varying gravitational field produced by a Weber bar is used to explore physical and mathematical features of the linearized Einstein equation. We present a self-contained formal framework for the treatment of the linear field, that is applicable to several sources for which the standard quadrupolar formulas are not adequate. The expressions for retarded integrals reveal a singularity associated with boundary conditions. Results from the transverse traceless subgauge are compared with the radiation calculated from retarded integrals. Lienard–Wiechert potentials are used in a treatment of the Weber bar as a collection of point particles and further possible applications are outlined. The Riemann tensor clarifies the transition from near-field geodesic forces to tidal forces in the far field.