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The Kinky Singularity Conjecture
Ta-Da!
To state the conjecture we first need a
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
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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