Axially symmetric two-body problem in general relativity. III. Bondi mass loss and the failure of the quadrupole formula

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Abstract
Suggested difficulties and criticism regarding earlier work is addressed. It is demonstrated that the rate of gravitational energy loss from the authors' model free-fall system employing the widely accepted Bondi method agrees precisely with the results described in prior works. Origins of the breakdown of the quadrupole formalism for free fall, previously indicated, are now delineated in detail. The role of source structure in the energy loss rate re-emerges, bringing into question much of the earlier work of others. The iterative technique with flat-space wave operators is justified. A new approach to quasiperiodic systems such as binary stars is described. Ideally modeled upon the actual birth of such systems, it evolves from an initially stationary configuration, again avoiding the problems and ambiguities regarding incoming radiation.

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