Identifying Riemannian singularities with regular non-Riemannian geometry

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.

v2) 7 pages, title modified, references added, redaction improved, example D relegated to Supplemental Material. To appear in Physical Review Letters

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Cited by in corpus (7)

• Torsional string Newton-Cartan geometry for non-relativistic strings
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• Fractons, non-Riemannian Geometry, and Double Field Theory
• Perturbations in $\mathbf{O}(D,D)$ string cosmology from double field theory
• Traversable wormhole for string, but not for particle
• Gravitational Core of Double Field Theory: Lecture Notes
• If you want to cross singularity, wrap it!