Lorentzian manifolds and scalar curvature invariants

Details Lorentzian manifolds and scalar curvature invariants Lorentzian manifolds and scalar curvature invariants

2010-03-11

arxiv.org/abs/1003.2373v1

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

submitted to CQG

Scientific paper

We discuss (arbitrary-dimensional) Lorentzian manifolds and the scalar polynomial curvature invariants constructed from the Riemann tensor and its covariant derivatives. Recently, we have shown that in four dimensions a Lorentzian spacetime metric is either $\mathcal{I}$-non-degenerate, and hence locally characterized by its scalar polynomial curvature invariants, or is a degenerate Kundt spacetime. We present a number of results that generalize these results to higher dimensions and discuss their consequences and potential physical applications.

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