  We derive new results on radiation, angular momentum at future null infinity
and peeling for a general class of spacetimes. For asymptotically-flat
solutions of the Einstein vacuum equations with a term homogeneous of degree
$-1$ in the initial data metric, that is it may include a non-isotropic mass
term, we prove new detailed behavior of the radiation field and curvature
components at future null infinity. In particular, the limit along the null
hypersurface $C_u$ as $t \to \infty$ of the curvature component $\rho =
\frac{1}{4} R_{3434}$ multiplied with $r^3$ tends to a function $P(u, \theta,
\phi)$ on $\mathbb{R} \times S^2$. When taking the limit $u \to + \infty$
(which corresponds to the limit at spacelike infinity), this function tends to
a function $P^+ (\theta, \phi)$ on $S^2$. We prove that the latter limit does
not have any $l=1$ modes. However, it has all the other modes, $l=0, l \geq 2$.
Important derivatives of crucial curvature components do not decay in $u$,
which is a special feature of these more general spacetimes. We show that
peeling of the Weyl curvature components at future null infinity stops at the
order $r^{-3}$, that is $r^{-4} |u|^{+1}$, for large data, and at order $r^{-
\frac{7}{2}}$ for small data. Despite this fact, we prove that angular momentum
at future null infinity is well defined for these spacetimes, due to the good
behavior of the $l=1$ modes involved.
