Abstract
In any theory of gravitation that predicts the existence of gravitational waves, it is shown that, in the absence of mass exchange and mass loss and subjected to a condition, a circular binary system with spherically-symmetrical components cannot evolve in such a way that the spin angular velocity is always a linear function of the orbital velocity. Probably this relation between the angular velocities cannot be realized in any time interval. In particular, the system cannot remain in a synchronized state. Of eight special cases of evolution of this binary system, three cases, where the separation increases, are shown to be kinematically impossible while a restriction on the variation of a parameter governing the evaluation of the system can be made in another. In one of the kinematically allowed special cases the separation increases.
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