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An infinitesimal coordinate change generated by ${\xi }_a$ acts on the trace-reversed metric perturbation asIts divergence changes bySolving $\square {\xi }_b={\partial }^a{\bar{h}}_{ab}$ therefore imposes Lorenz gauge in linearized gravity, ${\partial }^a{\bar{h}}_{ab}=0$. Transformations satisfying $\square {\xi }_b=0$ remain and form the residual gauge symmetry of linearized gravity.

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.