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The Bondi-Sachs formalism for the Einstein scalar field equations with the zero cosmological constant

Feb 6, 2024

32 pages

e-Print:

2402.04577 [gr-qc]

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Abstract: (arXiv)

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

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.

Note:

32 pages, revised version, to appear in Peking Mathematical Journal

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