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An analysis is presented of gravitational radiation from astrophysical bodies, in terms of an expansion in powers of (velocity), which equals approximately the square root of the Newtonian potential, within general relativity. Explicit expressions are obtained for the distant radiation field and energy flux from perfect-fluid sources, valid through 3/2 post-Newtonian order (beyond the usual formulae).
Epstein et al. (Thu,) studied this question.