The Kinky Singularity Conjecture

Ta-Da!

To state the conjecture we first need a

### Definition

Let (M,g) be an asymptotically flat spacetime which is topologically
of the form C x R, where R denotes the real line and C denotes
some asymptotically flat 3-surface which is everywhere spacelike
outside of some compact set U in C. Then we say that the
spacetime (M,g) describes an asymptotically flat kink if
kink(C;g) is non-vanishing (here, kink(C;g) denotes the kink
number of g relative to the surface C, i.e.,
kink(C;g) is the degree of the map from C to the three-sphere S(3),
which is defined by a timelike vector field V induced by g).

For a crude picture of an asymptotically flat kink, click
here.

Given this definition we can then state the

## Conjecture

**Let (M,g) be a chronological spacetime describing an asymptotically
flat kink and satisfying the strong and generic energy conditions.
Then (M,g) is timelike and null geodesically incomplete.**

If you manage to prove this, drop me a line!

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