Identifying Riemannian singularities with regular non-Riemannian geometry

TL;DR

This paper demonstrates that certain singular spacetimes in General Relativity can be understood as regular non-Riemannian geometries within Double Field Theory, revealing new insights into spacetime singularities and geodesic completeness.

Contribution

It identifies a class of singular spacetimes as regular non-Riemannian geometries in Double Field Theory, offering a novel perspective on singularities beyond Riemannian geometry.

Findings

Singularities correspond to coordinate singularities in non-Riemannian geometries.

Geodesics are complete outside the non-Riemannian sphere.

Particles freeze and strings become chiral near non-Riemannian points.

Abstract

Admitting non-Riemannian geometries, Double Field Theory extends the notion of spacetime beyond the Riemannian paradigm. We identify a class of singular spacetimes known in General Relativity with regular non-Riemannian geometries. The former divergences merely correspond to coordinate singularities of the generalised metric for the latter. Computed in string frame, they feature an impenetrable non-Riemannian sphere outside of which geodesics are complete with no singular deviation. Approaching the non-Riemannian points, particles freeze and strings become (anti-)chiral.