  Inspired by interaction of gravitational waves and dark matters, we study the
Bondi-Sachs formalism for Einstein massless scalar field with zero cosmological
constant. We provide asymptotic expansions for the Bondi-Sachs metrics as well
as the scalar fields and prove the peeling property. We also prove the
positivity of the Bondi energy-momentum under conditions ensuring certain
asymptotically null hypersurfaces are of order 2.
