Absence of covariant singularities in pure gravity

TL;DR

This paper proposes analyzing gravitational singularities in field space rather than spacetime, demonstrating that the field-space Kretschmann scalar remains finite, suggesting that singularities may be artifacts of variable choices rather than physical entities.

Contribution

It introduces a covariant approach to study singularities in field space, showing that the Kretschmann scalar can be finite, challenging the traditional view of singularities in pure gravity.

Findings

Field-space Kretschmann scalar is finite for a specific DeWitt metric

Vacuum singularities in GR may result from variable choices

Suggests no true singularities in pure gravity for any action

Abstract

The assumptions of the Hawking-Penrose singularity theorem are not covariant under field redefinitions. Thus we propose to study singularities in field space, where the spacetime metric is treated as a coordinate along with any other fields. We show that the field-space Kretschmann scalar for a certain choice of the DeWitt field-space metric is everywhere finite. This fact could be interpreted as an indication that no singularities actually exist in pure gravity for any gravitational action. In particular, all vacuum singularities of General Relativity result from an unhappy choice of field variables. The extension to the case in which matter fields are present, as required by singularity theorems, is left for future development.