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Type: Journal article
Title: Conformal pure radiation with parallel rays
Author: Leistner, T.
Nurowski, P.
Citation: Classical and Quantum Gravity, 2012; 29(5):055007-1-055007-15
Publisher: IOP Publishing Ltd
Issue Date: 2012
ISSN: 0264-9381
Statement of
Thomas Leistner and Paweł Nurowski
Abstract: We define pure radiation metrics with parallel rays to be n-dimensional pseudo-Riemannian metrics that admit a parallel null line bundle K and whose Ricci tensor vanishes on vectors that are orthogonal to K. We give necessary conditions in terms of the Weyl, Cotton and Bach tensors for a pseudo-Riemannian metric to be conformal to a pure radiation metric with parallel rays. Then, we derive conditions in terms of the tractor calculus that are equivalent to the existence of a pure radiation metric with parallel rays in a conformal class. We also give analogous results for n-dimensional pseudo-Riemannian pp-waves.
Rights: © 2012 IOP Publishing Ltd
RMID: 0020116819
DOI: 10.1088/0264-9381/29/5/055007
Appears in Collections:Mathematical Sciences publications

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