Abstract
The main thrust of this paper is on real vacuum (single) Kerr-Schild (VKS) metrics. The conditions are given for real VKS metrics to have twistfree expanding principal null directions and to have Weyl tensors of Petrov type $D$. It follows that there are no twistfree type $II$ metrics i.e. no Robinson-Trautman ones. VKS metrics with twist either belong to the Kerr family or else are of type $II$. Non-expanding VKS metrics are of type $N$. The condition for a VKS metric to be of type $D$ leads naturally to a complex translation which has been used to obtain the Kerr metric from the Schwarzschild metric.
Information
Published: 1 January 1989
First available in Project Euclid: 18 November 2014
zbMATH: 0681.53049
MathSciNet: MR1020800
Rights: Copyright © 1989, Centre for Mathematics and its Applications, Mathematical Sciences Institute, The Australian National University. This book is copyright. Apart from any fair dealing for the purpose of private study, research, criticism or review as permitted under the Copyright Act, no part may be reproduced by any process without permission. Inquiries should be made to the publisher.
