Abstract
A nonsingular, sourceless, first-order pulse of gravitational radiation imploding from infinity to a focus and then exploding back out to infinity is examined to second order. It is found that, contrary to what might be expected, the nonsingular second-order field contains no radiation. In space-time regions outside of the pulse, the second-order field is nonvanishing only in the region with retarded times earlier than the passing of the exploding pulse and advanced times later than the passing of the imploding pulse. In this region, the second-order field is that of a Schwarzschild mass, plus a nonradiative quadrupole, plus a nonradiative sixteen pole.
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