All metrics have curvature tensors characterised by its invariants as a   limit: the \epsilon-property
  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. 
Sigbjorn Hervik
gr-qc hep-th math-ph math.MP