  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.
