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

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

2011-07-16

arxiv.org/abs/1107.3210v1

Class.Quant.Grav.28:157001,2011

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

6 pages

Scientific paper

10.1088/0264-9381/28/15/157001

We prove a generalisation of the $\epsilon$-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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