The effect of gravitational radiation-reaction on the evolution of the Riemann S-type ellipsoids

It is shown that the -post-Newtonian formalism for describing gravitational radiation-reaction is equivalent to the formalism developed by Burke and Thorne, if one is neglecting lower-order post-Newtonian corrections. Since the radiation-reaction terms are then expressible as a gradient, the circulation of a fluid is not altered by the emission of gravitational radiation; from this conservation law it may be seen that a Jacobi ellipsoid, as it evolves by gravitational radiation, cannot remain on the Jacobi sequence. The equations of motion governing the evolution by radiationreaction of the Jacobi ellipsoid and other Riemann S-type ellipsoids are integrated for several initial configurations. Evolution proceeds toward a nonradiating state which in some cases is a Maclaurin spheroid and in other cases a Dedekind ellipsoid. Subject headings: gravitation - relativity - rotation