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One basic part of determining a metric (or applicable generalization) of a given set $\cal S$ of events (up to an arbitrary non-zero constant) is to determine to which pairs among those events, $\mathscr P, \mathscr Q \in \cal S$, to assign the (suitably generalized) distance value $s[ \mathscr P, \mathscr Q ] = s[ \mathscr Q, \mathscr P ] = 0$.

In general relativity, is this assignment for two such events $\mathscr P$ and $\mathscr Q$ made if and only if event $\mathscr Q$ is 'on the light cone of' event $\mathscr P$, and vice versa event $\mathscr P$ is 'on the light cone of' event $\mathscr Q$;
i.e. in the (physics related) terminology of H. Minkowski, "Raum und Zeit", (1909):
if and only if "one event had sent light towards the other, or had received light from the other" ?

user12262
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Yes, that is quite right. A 'null' separation between two events is also called 'lightlike' since it implies that the points are on each other's light cone (the property is symmetric; it is in fact an equivalence relation now that I think about it)

Danu
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