Covariant singularities: a brief review

TL;DR

This paper reviews covariant singularities, emphasizing their invariance under both spacetime diffeomorphisms and field redefinitions, questioning the traditional notion of singularities in general relativity.

Contribution

It introduces and discusses the concept of covariant singularities, highlighting their importance for understanding the true nature of singularities in a covariant framework.

Findings

Hawking-Penrose theorem is not covariant under field redefinitions

Covariant singularities are invariant under both diffeomorphisms and field redefinitions

The invariance principle challenges traditional views on spacetime singularities

Abstract

The Hawking-Penrose theorem is not covariant under field redefinitions. Should the invariance under such transformations be a true principle in Nature, spacetime singularities become dubious objects. We here review the concept of covariant singularities, that is, singularities that are invariant under both spacetime diffeomorphisms and field redefinitions.