Conformal pure radiation with parallel rays

Details Conformal pure radiation with parallel rays Conformal pure radiation with parallel rays

2011-07-08

arxiv.org/abs/1107.1675v2

Mathematics

Differential Geometry

14 pages, in v2 Remark 2 about integrability conditions added

Scientific paper

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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