Solution
= Solution
In <Lorenz gauge>, $\partial_\mu\bar h^{\mu\nu}=0$. A leading outgoing far-zone field depends on retarded time $u=t-r$, so $\partial_j=-\widehat x_j\partial_u+O(r^{-1})$. Taking $\nu=i$ and using $\bar h^{0i}=-\bar h_{0i}$ gives
$$
\partial_u\bar h_{0i}=-\widehat x_j\partial_u\bar h_{ji}.
$$
Dropping a nonradiative integration constant and using part i,
$$
\boxed{\bar h_{0i}(t,\mathbf x)
\simeq-\frac{2\widehat x_j}{r}\ddot I_{ij}(t-r)}.
$$