On space-times which cannot be distinguished by curvature invariants

TL;DR

This paper demonstrates that certain non-isometric space-times with non-zero curvature scalars cannot be distinguished using curvature invariants, highlighting limitations in the invariants' discriminative power.

Contribution

It provides a specific example of space-times that share identical curvature invariants despite being non-isometric, revealing a fundamental limitation.

Findings

Non-isometric space-times can have identical curvature invariants

Curvature invariants may not uniquely identify space-time geometries

Example with non-vanishing curvature scalar illustrates this limitation

Abstract

We present an example that non-isometric space-times with non-vanishing curvature scalar cannot be distinguished by curvature invariants.