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

Anton S Galaev (1) , Thomas Leistner (2)

1 SCI / MUNI - Faculty of Science [Brno]
2 School of Mathematical Sciences

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.

Mots clés: Physical Sciences

Anton S Galaev, Thomas Leistner. On the local structure of Lorentzian Einstein manifolds with parallel distribution of null lines. Classical and Quantum Gravity, 2010, 27 (22), pp.225003. ⟨10.1088/0264-9381/27/22/225003⟩. ⟨hal-00643033⟩