  Scattering for the energy critical non-linear wave equation for domains
exterior to non trapping obstacles in 3+1 dimension is known for the
star-shaped case. In this paper, we extend the scattering for a class of non
star-shaped obstacles called illuminated from exterior. The main tool we use is
the method of multipliers with weights that generalize the Morawetz multiplier
to suit the geometry of the obstacle.
