Conformal transformations and Nordstr\"om's scalar theory of gravity

TL;DR

This paper explores Nordström's scalar gravity theory, highlighting its role as a non-minimal matter coupling example and examining how conformal transformations might extend manifolds through singularities.

Contribution

It demonstrates the potential of conformal transformations to extend manifolds in Nordström's theory, despite its observational disfavor.

Findings

Conformal transformations can extend manifolds through curvature singularities.

Nordström's theory exemplifies non-minimal matter coupling.

The theory is observationally ruled out.

Abstract

As we shall briefly recall, Nordstr\"om's theory of gravity is observationally ruled out. It is however an interesting example of non-minimal coupling of matter to gravity and of the role of conformal transformations. We show in particular that they could be useful to extend manifolds through curvature singularities.