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.

arXiv commentv2) 7 pages, title modified, references added, redaction improved, example D relegated to Supplemental Material. To appear in Physical Review Letters

References in corpus (57)

• Double Field Theory
• String Solitons
• Generalized metric formulation of double field theory
• Superspace Duality in Low-Energy Superstrings
• A Geometry for Non-Geometric String Backgrounds
• Duality, Quotients, and Currents
• Two-Vierbein Formalism for String-Inspired Axionic Gravity
• Background independent action for double field theory
• Doubled Geometry and T-Folds
• The gauge algebra of double field theory and Courant brackets
• Non-Relativistic Closed String Theory
• Supergravity as Generalised Geometry I: Type II Theories
• The (pseudo)issue of the conformal frame revisited
• Torsional Newton-Cartan Geometry and Lifshitz Holography
• Differential geometry with a projection: Application to double field theory
• Stringy differential geometry, beyond Riemann
• Non-Relativistic Superstrings: A New Soluble Sector of AdS_5xS^5
• Generalized Duality in Curved String-Backgrounds
• Non-Relativistic Strings and Limits of the AdS/CFT Correspondence
• IIA/B, Wound and Wrapped
• Horava-Lifshitz Gravity From Dynamical Newton-Cartan Geometry
• Global Aspects of T-Duality, Gauged Sigma Models and T-Folds
• On the Riemann Tensor in Double Field Theory
• Strings with Non-Relativistic Conformal Symmetry and Limits of the AdS/CFT Correspondence
• Nonrelativistic String Theory and T-Duality
• Covariant action for a string in doubled yet gauged spacetime
• Stringy Unification of Type IIA and IIB Supergravities under N=2 D=10 Supersymmetric Double Field Theory
• Conformal transformations in classical gravitational theories and in cosmology
• String Theory and String Newton-Cartan Geometry
• Comments on double field theory and diffeomorphisms
• Geodesic completeness in a wormhole spacetime with horizons
• Negative Branes, Supergroups and the Signature of Spacetime
• Relating non-relativistic string theories
• A Non-Relativistic Limit of NS-NS Gravity
• Strings and Branes are Waves
• String and Fivebrane Solitons: Singular or Non-singular?
• A non-relativistic limit of M-theory and 11-dimensional membrane Newton-Cartan geometry
• A worldsheet supersymmetric Newton-Cartan string
• Einstein Double Field Equations
• On Spherically Symmetric String Solutions in Four Dimensions
• $\mathbf{O}(D,D)$ Covariant Noether Currents and Global Charges in Double Field Theory
• Remarks on the non-Riemannian sector in Double Field Theory
• Non-Riemannian geometry of M-theory
• Weyl invariance of string theories in generalized supergravity backgrounds
• Green-Schwarz superstring on doubled-yet-gauged spacetime
• The rotation curve of a point particle in stringy gravity
• String Theory and non-Riemannian Geometry
• Non-Riemannian isometries from double field theory
• Non-Riemannian gravity actions from double field theory
• Timelike U-dualities in Generalised Geometry
• Conserved Currents of Double Field Theory
• Black hole thermodynamics, stringy dualities and double field theory
• Type II chiral affine Lie algebras and string actions in doubled space
• Doubled strings, negative strings and null waves
• Stringy Gravity: Solving the Dark Problems at `short' distance
• Causal structures and dynamics of black-hole-like solutions in string theory
• A note on Faddeev--Popov action for doubled-yet-gauged particle and graded Poisson geometry

Cited by in corpus (7)

• Torsional string Newton-Cartan geometry for non-relativistic strings
• Pregeometric First Order Yang-Mills Theory
• 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!