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At least about the definition of is a "complete future null infinity" I found some answers on the 8th page of these lectures by Klainerman.

I would be glad to hear of some explanations about how the two definitions given on that page relate to each other and how are they related to the notion explained by Tim in the comments to his answer. (Tim is calling the future null infinity to be complete if the whole manifold is geodesically complete)

Also these seem closely related to the idea of of calling a hypersurface as being "generated by complete null geodesics". I would like to know what this means and why this is often used as a condition for the event horizon to satisfy.

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At least about the definition of is a "complete future null infinity" I found some answers on the 8th page of these lectures by Klainerman.

I would be glad hear of some explanations about how the two definitions given on that page relate to each other and how are they related to the notion explained by Tim in the comments to his answer. (Tim is calling the future null infinity to be complete if the whole manifold is geodesically complete)

Also these seem closely related to the idea of of calling a hypersurface as being "generated by complete null geodesics". I would like to know what this means and why this is often used as a condition for the event horizon to satisfy.