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On Waylen's Regular Axisymmetric Similarity Solutions
Journal article   Peer reviewed

On Waylen's Regular Axisymmetric Similarity Solutions

Edward D. Fackerell and David P Hartley
General relativity and gravitation, Vol.32(5), pp.856-864
05/2000
DOI: 10.1023/A:1001980923501
url
https://arxiv.org/pdf/gr-qc/9809082View
Open Access

Abstract

We review the similarity solutions proposed by Waylen for a regular time–dependent axisymmetric vacuum space–time, and show that the key equation introduced to solve the invariant surface conditions is related by a Bäcklund transform to a restriction on the similarity variables. We further show that the vacuum space–times produced via this path automatically possess a (possibly homothetic) Killing vector, which may be time–like.

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