The Source-Decomposed Formulae of Linearized Gravitational-Wave Generation

In this research, the source structure of the linearized metric perturbation is revisited. We decompose the spatial source integral into additional five terms. The contributions of the additional five terms to the generation of gravitational waves are derived from Einstein’s linearized theory, which has not been completely mentioned previously. These contributions depend on the position, velocity, acceleration, density variation, and energy flow. The purpose of representing the source integral in terms of density change, velocity, acceleration, and energy flow contribution is to clarify how different source properties enter the linearized metric perturbation before the application of transverse-traceless (TT) projection. The observable gravitational radiation is from the TT-projected parts. These five terms are source-level contributions to the metric perturbation, and not every component of the metric perturbation corresponds to a radiative gravitational-wave degree of freedom before imposing the TT projection. Therefore, we propose three physical examples to demonstrate how gravitational waves are generated from these additional terms. The work is a useful analytical decomposition of source terms in linearized gravity.