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arXiv · 1003.2373

Lorentzian manifolds and scalar curvature invariants

Alan Coley·Sigbjorn Hervik·Nicos Pelavas
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Abstract

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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Alan Coley, Sigbjorn Hervik, Nicos Pelavas. 2010-03-11. Lorentzian manifolds and scalar curvature invariants. https://doi.org/10.1088/0264-9381%2F27%2F10%2F102001

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