All metrics have curvature tensors characterised by its invariants as a limit: the ϵ-property
Original version
Hervik, S. (2011). All metrics have curvature tensors characterised by its invariants as a limit: the ϵ-property. Classical and Quantum Gravity, 28(15) doi:10.1088/0264-9381/28/15/157001Abstract
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.
Description
This is an author-created, un-copyedited version of an article accepted for publication in Classical and quantum gravity. IOP Publishing Ltd is not responsible for any errors or omissions in this version of the manuscript or any version derived from it. The Version of Record is available online at doi:10.1088/0264-9381/28/15/157001.