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Regular Type III and Type N Approximate Solutions

Philip Downes·Paul MacAllevey·Bogdan Nita·Ivor Robinson
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Abstract

New type III and type N approximate solutions which are regular in the linear approximation are shown to exist. For that, we use complex transformations on self-dual Robinson-Trautman metrics rather then the classical approach. The regularity criterion is the boundedness and vanishing at infinity of a scalar obtained by saturating the Bel-Robinson tensor of the first approximation by a time-like vector which is constant with respect to the zeroth approximation.

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Philip Downes, Paul MacAllevey, Bogdan Nita, Ivor Robinson. 2001-05-18. Regular Type III and Type N Approximate Solutions. https://arxiv.org/abs/gr-qc/0105064

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