The Bondi-Sachs formalism for the Einstein scalar field equations with the zero cosmological constant
Abstract
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 condition c=d=0 at some retarded time u0. This condition ensures that asymptotically null hypersurfaces near u=u0 are asymptotically null initial data sets of order 2 and the positive energy theorem for null infinity can be applied.
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