A linearized Einstein-Maxwell field composed of a mass monopole, a radiating mass quadrupole, a Coulomb field, and radiating electromagnetic dipole and quadrupole fields is examined to second order. If the first-order radiation is a pulse of finite duration, then the only second-order radiation present after the pulse has turned off is due to interactions involving the mass monopole. All other interactions contributing to the second order produce no such scattered radiation. At third order, the dipole-dipolemass interaction is found to give rise to scattered radiation.
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Couch et al. (1971) studied this question.
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