  We study a defocusing semilinear wave equation, with a power nonlinearity
$|u|^{p-1}u$, defined outside the unit ball of $\mathbb{R}^{n}$, $n\ge3$, with
Dirichlet boundary conditions. We prove that if $p>n+4$ and the initial data
are nonradial perturbations of large radial data, there exists a global smooth
solution. The solution is unique among energy class solutions satisfying an
energy inequality. The main tools used are the Penrose transform and a
pointwise decay estimate for the exterior linear wave equation perturbed with a
large, time dependent potential.
