1210.6920 (Robert Milson et al.)

Three-dimensional spacetimes of maximal order    [PDF]

Robert Milson, Lode Wylleman

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.

View original: http://arxiv.org/abs/1210.6920