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arXiv · 1210.6920

Three-dimensional spacetimes of maximal order

Robert Milson·Lode Wylleman
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Abstract

We show that the equivalence problem for three-dimensional Lorentzian manifolds requires at most the fifth covariant derivative of the curvature tensor. We prove that this bound is sharp by exhibiting a class of 3D Lorentzian manifolds which realize this bound. The analysis is based on a three-dimensional analogue of the Newman-Pen-rose formalism, and spinorial classification of the three-dimensional Ricci tensor.

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Robert Milson, Lode Wylleman. 2012-10-25. Three-dimensional spacetimes of maximal order. https://doi.org/10.1088/0264-9381/30/9/095004

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