On the local structure of Lorentzian Einstein manifolds with parallel distribution of null lines

Abstract

We study transformations of coordinates on a Lorentzian Einstein manifold with a parallel distribution of null lines and show that the general Walker coordinates can be simplified. In these coordinates, the full Lorentzian Einstein equation is reduced to equations on a family of Einstein Riemannian metrics.

Dedicated to Dmitri Vladimirovich Alekseevsky on his 70th birthday

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Cited by in corpus (15)

• Completeness of compact Lorentzian manifolds with Abelian holonomy
• Two-symmetric Lorentzian manifolds
• On the Weyl Tensor Classification in All Dimensions and its Relation with Integrability Properties
• Examples of Einstein spacetimes with recurrent null vector fields
• The curvature of almost Robinson manifolds
• Some applications of the Lorentzian holonomy algebras
• Classification of third-order symmetric Lorentzian manifolds
• Parallel spinors on Lorentzian Weyl spaces
• Geometry and holonomy of indecomposable cones
• How to find the holonomy algebra of a Lorentzian manifold
• Spinors of real type as polyforms and the generalized Killing equation
• Conformally flat Lorentzian manifolds with special holonomy groups
• On the Geometry of Circle Bundles with Special Holonomy
• On the splitting problem for Lorentzian manifolds with an $\mathbb{R}$-action with causal orbits
• Decomposable $(5,6)$-solutions in eleven-dimensional supergravity