Inspired by interaction of gravitational waves and dark matters, we study the Bondi-Sachs metrics 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 positivity of the Bondi energy-momentum under condition c=d=0 at some retarded time u_0. This condition ensures that asymptotically null hypersurfaces near u=u_0 are asymptotically null initial data sets of order 2 and the positive energy theorem for null infinity can be applied. The talk is based on the joint work with Jialue Li.
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