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arXiv · 1107.1675

Conformal pure radiation with parallel rays

Thomas Leistner·Pawel Nurowski
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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 tractor calculus that are equivalent to the existence of a pure radiation metric with parallel rays in a conformal class. We also give an analogous result for n-dimensional pseudo-Riemannian pp-waves.

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Thomas Leistner, Pawel Nurowski. 2011-07-28. Conformal pure radiation with parallel rays. https://doi.org/10.1088/0264-9381%2F29%2F5%2F055007

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