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 (8)

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Cited by in corpus (11)

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• Spinor-helicity and the algebraic classification of higher-dimensional spacetimes
• A Goldberg-Sachs theorem in dimension three
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• On the Equivalence of Spacetimes, the Cartan-Karlhede Algorithm
• On scalar curvature invariants in three dimensional spacetimes
• Scalar Polynomial Curvature Invariants in the Context of the Cartan-Karlhede Algorithm
• Cotton Double Copy for Gravitational Waves
• Observer-based invariants for cosmological models
• Impulsive gravitational waves in general massive 3D gravity