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

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

2009-12-17

arxiv.org/abs/0912.3400v3

Class. Quantum Grav. 27 (2010) 225003

Mathematics

Differential Geometry

Dedicated to Dmitri Vladimirovich Alekseevsky on his 70th birthday

Scientific paper

10.1088/0264-9381/27/22/225003

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.

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