Dual geometries and spacetime singularities

TL;DR

This paper explores how dual geometrical frameworks in Brans-Dicke and general relativity can eliminate spacetime singularities, offering a physically equivalent but singularity-free perspective of the universe.

Contribution

It demonstrates that certain solutions in dual geometrical theories can avoid singularities present in standard general relativity.

Findings

Singularities can be avoided in dual Weyl-type geometries.

Dual representations are physically equivalent to standard GR.

Provides a new perspective on spacetime singularities.

Abstract

The notion of geometrical duality is discussed in the context of both Brans-Dicke theory and general relativity. It is shown that, in some particular solutions, the spacetime singularities that arise in usual Riemannian general relativity may be avoided in its dual representation (Weyl-type general relativity). This dual representation provides a singularity-free picture of the World that is physicaly equivalent to the canonical general relativistic one.