Axially symmetric two-body problem in general relativity. II. Free fall

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Abstract
The analysis of the two-body problem from an initially static configuration, initiated by one of the authors, is extended to free fall. Fluid model sources held apart by a strut are introduced and the strut is severed. The dynamic metric perturbation is found with the required continuity and no singularities when the complementary phenomena of stress breaking in the strut, pressure variation in the bodies, and the ensuing free-fall motion are properly synthesized. Nonlinear contributions to the metric are shown to lead to a gravitational energy flux in free fall which dominates that which one would expect from the Einstein quadrupole formula. The reasons for the failure of the quadrupole formula for free fall are indicated.

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