What are the main definitions of timelike and lightlike curves in Minkowski 3-space?
There are some articles about closed timelike and lightlike curves. But there is a survey " https://arxiv.org/pdf/0810.3351.pdf " says "There are not closed curves in Minkowski 3-space that are timelike or lightlike". Which one is true? Any explanation?
Thank you. What do you mean we need curvature or nontrivial topology? Do you have an example?
In the anti de sitter space,i.e,one with a negative curvature you can see closed timelike curves...so by coordinate transformation we go to its covering space where the curves are unfolded... check pg-87 of the file attached
Dear Ferhat,
Any closed curve in this three dimensional Minkowski space must belong on the surface of a spheroid. I imagine an almost time-like closed curve if it is very much elongated along the time axis and an almost space-like if the elongation is along one of the spatial axes.
Cheers,
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