Unattainable extended spacetime regions in conformal gravity

TL;DR

This paper demonstrates that conformal gravity can resolve singularities present in certain Einstein gravity solutions, making the spacetime complete and removing the naked singularities.

Contribution

It shows how choosing a suitable conformal factor in conformal gravity can eliminate singularities in specific spacetime solutions.

Findings

Curvature invariants remain finite in conformal gravity.

Massive particles cannot reach the original singular surface.

Massless particles cannot reach the singularity with finite affine parameter.

Abstract

The Janis-Newman-Winicour metric is a solution of Einstein's gravity minimally coupled to a real massless scalar field. The $\gamma$-metric is instead a vacuum solution of Einstein's gravity. These spacetimes have no horizon and possess a naked singularity at a finite value of the radial coordinate, where curvature invariants diverge and the spacetimes are geodetically incomplete. In this paper, we reconsider these solutions in the framework of conformal gravity and we show that it is possible to solve the spacetime singularities with a suitable choice of the conformal factor. Now curvature invariants remain finite over the whole spacetime. Massive particles never reach the previous singular surface and massless particles can never do it with a finite value of their affine parameter. Our results support the conjecture according to which conformal gravity can fix the singularity problem that plagues Einstein's gravity.