Smooth metrics can hide thin shells

TL;DR

This paper reveals that smooth metric tensors suggesting wormholes with zero curvature are misleading, as they are typically supported by exotic thin shells in general relativity.

Contribution

It demonstrates that smooth-looking metrics implying wormholes actually require thin shells, clarifying misconceptions about their physical plausibility.

Findings

Smooth metrics can conceal thin shells supporting wormholes

Vanishing curvature does not imply absence of matter sources

Exotic matter is necessary for such wormhole solutions

Abstract

In this note, I consider a class of metric tensors with smooth components that naively appear to describe dynamical wormholes with vanishing spacetime curvature. I point out that the smoothness of the metric tensor components is deceptive, and that in general relativity, such metrics must be sourced by exotic thin shells.