"Singularities" in spacetimes with diverging higher-order curvature invariants

TL;DR

This paper investigates the relationship between diverging higher-order curvature invariants and singularities in spacetimes, demonstrating that such divergences do not always indicate classical or quantum singularities when zeroth-order invariants are regular.

Contribution

It provides examples showing that diverging higher-order invariants alone do not necessarily imply singularities, challenging previous assumptions.

Findings

Diverging higher-order invariants do not always indicate singularities.

Regular zeroth-order invariants can coexist with diverging higher-order invariants.

Examples demonstrate the disconnect between invariant divergence and singularity presence.

Abstract

After reviewing the definitions of classical and quantum singularities, it is shown by example that if zeroth-order curvature invariants are regular, a diverging higher-order curvature invariant does not necessarily imply the existence of a classical or a quantum singularity.