\item Non-radiative metric perturbation $h_{\mu\nu}$ can not be put into TT form (discussed in the class). For example, consider the external field of a non rotating spherical star of mass $M$ (Newtonian source, velocities slow enough to neglect retardation). Calculate the metric perturbation in the weak field limit and show that there are non radiative metric perturbations that can not be transformed into TT form. \\
\textit{Hint}: General solution to linearized field equation in Lorentz gauge,
\item Non-radiative metric perturbation $h_{\mu\nu}$ can not be put into TT form (discussed in the class). For example, consider the external field of a non rotating spherical star of mass $M$ (Newtonian source, velocities slow enough to neglect retardation). Calculate the metric perturbation in the weak field limit and show that there are non radiative metric perturbations that can not be transformed into TT form. \textit{Hint}: General solution to linearized field equation in Lorentz gauge,