 Manifolds are great for representing events. But the metric \(g\) dictates how these events are related. Is it possible for a person to travel from this event to that one? If so, how much elapsed time does a person record between them? The metric \(g\) tells us. At each event, \(g\) assigns a double cone structure. The cone structures can change from event to event; we only require that they do so smoothly. Usually, one works with models of general relativity in which one can label the two lobes of each double cone as “past” and “future” in a way which involves no discontinuities. We will do so in what follows. (See figure 2.1.1.) 