Regular Type III and Type N Approximate Solutions

Details Regular Type III and Type N Approximate Solutions Regular Type III and Type N Approximate Solutions

2001-05-18

arxiv.org/abs/gr-qc/0105064v1

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

6 pages, no figures

Scientific paper

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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