Events are never curved!
I've seen something that seems similar like what some are talking about here described as[1]:
"If a spacetime is not time-orientable then a closed path exists round which the direction of time reverses. The simplest example of non-orientability is the Mobius strip. On the Mobius strip left-handed and right-handed cannot be consistently defined over the whole surface. A left-handed coordinate basis changes to a night- handed one when going round the circumference of the strip.
The Mobius band can also be thought of as a spacetime diagram for a circular space, S1, and a non-orientable time. The direction of time reverses on a path around the circumference S1 of the band. Note that our usual image of a Mobius strip is as a 2D surface embedded in 3D. However the embedding is not unique and the Mobius can be defined in a number of ways without resorting to any embedding at all.
More importantly, it has topological properties (The non orientability) that can be described independently of the embedding. Of particular interest is a model of a particle as an asymptotically flat spacetime manifold with a region of non trivial topology where time is not orientable."
But its hard for me to come up with a term that can encompass a particle and a black hole (i'm sure there has to be one out there), in different regions in an asymptotically flat spacetime manifold, but exist in the same non trivial topology where time is not orientable.
[0] https://physics.stackexchange.com/questions/3656/can-spaceti...