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On the type N twisting vacuum solution of the Einstein equations

One of the problems in the catalogue of solutions to the vacuum solutions of the Einstein equations is the dearth of solutions to what is known as the type N twisting metric. Were it to be found in its general form it would then, according to the Peeling theorem of Sachs (Proc R Soc Lond A270:103, 1...

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Published in:General relativity and gravitation 2017-10, Vol.49 (10), p.1-7, Article 127
Main Author: Held, A.
Format: Article
Language:English
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Summary:One of the problems in the catalogue of solutions to the vacuum solutions of the Einstein equations is the dearth of solutions to what is known as the type N twisting metric. Were it to be found in its general form it would then, according to the Peeling theorem of Sachs (Proc R Soc Lond A270:103, 1962 ), describe the asymptotic gravitational field of an isolated source. The only known mathematical solution was found by Hauser (Phys Rev Lett 33:1112, 1974 ) and (Phys Rev Lett 33:1525, 1974 ). In this article the general equations are reduced to one third order complex equation for one complex variable plus one simple condition.
ISSN:0001-7701
1572-9532
DOI:10.1007/s10714-017-2274-z