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arXiv · 1107.3210

All metrics have curvature tensors characterised by its invariants as a limit: the ε-property

Sigbjorn Hervik
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Abstract

We prove a generalisation of the $ε$-property, namely that for any dimension and signature, a metric which is not characterised by its polynomial scalar curvature invariants, there is a frame such that the components of the curvature tensors can be arbitrary close to a certain "background". This "background" is defined by its curvature tensors: it is characterised by its curvature tensors and has the same polynomial curvature invariants as the original metric.

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Sigbjorn Hervik. 2011-07-16. All metrics have curvature tensors characterised by its invariants as a limit: the ε-property. https://doi.org/10.1088/0264-9381%2F28%2F15%2F157001

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