Three-dimensional spacetimes of maximal order

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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References in corpus (4)

• Type D Solutions of 3D New Massive Gravity
• The type N Karlhede bound is sharp
• A Petrov type I and generically asymmetric rotating dust family
• Lie Algebroids and Classification Problems in Geometry