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There are two types of event cone - self-orientated and event-orientated (the object at the point of the cones). The difference is merely one of perception.

The best way of visualising an event cone is to imagine a star going nova, shooting off interstellar matter (and light) in all directions. These can be visualised as spheres around the star expanding at different speeds. The light event cone is expanding fastest (at 3x108 ms-1, the speed of light). When this sphere reaches a point, at that point of time that place can recognise the event... that the star has gone nova. Before this happens, they have no idea.

Wormholes tend to mess event cones up... imagine a wormhole labelled $-$..

    |\       /   \ 2 /
    | \     /     \ /   
    |  \  $/       $
    |   \ /       / \ 
time|    X       /   \    
    |   / \     /     \   
    |  /   \   /       \ 
    | /     \ /         \  
    |/       \  
    +---------------------
          space
Area 2 is outside of X's main event cone, but any light coming through the wormhole is visible here... they can detect that it has gone nova. If the wormhole has different entry and exit times then it is possible to give people hints that the star is going to go nova (if the wormhole's exit is in the star's history event cone...
    |\       /
    | \     /
    |  \  $/
    |\  \ /  /
    | \  X  /
    |  \/ \/
    |  /\3/\
    | /  $  \
    |/  / \  \
In region 3 they have information from the wormhole that the star will go nova and can evacuate...
Is the correct name hypercone?