Basis for scalar curvature invariants in three dimensions

Abstract

$\mathcal{I}$-non-degenerate spaces are spacetimes that can be characterized uniquely by their scalar curvature invariants. The ultimate goal of the current work is to construct a basis for the scalar polynomial curvature invariants in three dimensional Lorentzian spacetimes. In particular, we seek a minimal set of algebraically independent scalar curvature invariants formed by the contraction of the Riemann tensor and its covariant derivatives up to fifth order of differentiation. We use the computer software \emph{Invar} to calculate an overdetermined basis of scalar curvature invariants in three dimensions. We also discuss the equivalence method and the Karlhede algorithm for computing Cartan invariants in three dimensions.

20 pages

References in corpus (5)

• The Invar tensor package: Differential invariants of Riemann
• Irreducible forms for the metric variations of the action terms of sixth-order gravity and approximated stress-energy tensor
• Three-dimensional spacetimes of maximal order
• Isometries in higher dimensional CCNV spacetimes
• Killing vectors in higher dimensional spacetimes with constant scalar curvature invariants