Comparison of metrics from retarded integrals and transverse traceless subgauge

TL;DR

This paper compares different metric calculation methods in linearized gravity, focusing on retarded integrals and transverse traceless subgauge, to better understand gravitational radiation from systems like Weber bars.

Contribution

It introduces a formal framework for linear gravitational fields applicable beyond standard quadrupolar formulas, analyzing boundary singularities and comparing gauge approaches.

Findings

Retarded integrals exhibit boundary-related singularities.

Transverse traceless subgauge results align with retarded integral calculations.

Lienard-Wiechert potentials effectively model Weber bars as point particles.

Abstract

The time-varying gravitational field produced by a Weber bar is used to explore mathematical features of the linearized Einstein equation. We present a self-contained formal framework for the treatment of the linear field, which is applicable to several situations where 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.