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

Abstract

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.

arXiv comment6 pages

References in corpus (8)

• Spacetimes characterized by their scalar curvature invariants
• Kundt Spacetimes
• New supersymmetric AdS_3 solutions
• Relativistic gyratons in asymptotically AdS spacetime
• Curvature operators and scalar curvature invariants
• Exact Wave Solutions to 6D Gauged Chiral Supergravity
• The type N Karlhede bound is sharp
• VSI_i spacetimes and the epsilon-property

Cited by in corpus (1)

• A spacetime not characterised by its invariants is of aligned type II