Radiation boundary condition for linearized gravity Created 2026-10-07 Updated 2026-10-14
The retarded source solution of the Linearized Einstein equations is selected by excluding added incoming or freely specified homogeneous gravitational waves. A homogeneous wave can satisfy Lorenz gauge in linearized gravity while having no source mass quadrupole moment. Thus a formula for the retarded source field is not an identity for every solution of the sourced wave equation.
Retarded quadrupole field Created 2026-10-05 Updated 2026-10-07
For a compact slowly moving source in the weak-field approximation, with no incoming homogeneous wave and , the retarded Linearized Einstein equations give this leading far-zone trace-reversed metric perturbation. The key consequence of stress-energy conservation is . The physical gravitational wave is obtained by the transverse-traceless projector.