Conformal pure radiation with parallel rays

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.

14 pages, in v2 Remark 2 about integrability conditions added

References in corpus (1)

• Ambient metrics for $n$-dimensional $pp$-waves

Cited by in corpus (5)

• Isotropic quasi-Einstein manifolds
• Conformal superalgebras via tractor calculus
• Conformal holonomy, symmetric spaces, and skew symmetric torsion
• On the conformal transformation between two anisotropic fluid spacetimes
• The ambient obstruction tensor and conformal holonomy