Editing General relativity (section)

=== Causal structure and global geometry ===
{{Main|Causal structure}}
[[File:Penrose.svg|thumb|Penrose–Carter diagram of an infinite [[Minkowski space|Minkowski universe]]]]
In general relativity, no material body can catch up with or overtake a light pulse. No influence from an event ''A'' can reach any other location ''X'' before light sent out at ''A'' to ''X''. In consequence, an exploration of all light worldlines ([[Geodesics in general relativity|null geodesics]]) yields key information about the spacetime's causal structure. This structure can be displayed using [[Penrose diagram|Penrose–Carter diagrams]] in which infinitely large regions of space and infinite time intervals are shrunk ("[[Compactification (mathematics)|compactified]]") so as to fit onto a finite map, while light still travels along diagonals as in standard [[spacetime diagram]]s.<ref>{{Harvnb|Frauendiener|2004}}, {{Harvnb|Wald|1984|loc=sec. 11.1}}, {{Harvnb|Hawking|Ellis|1973|loc=sec. 6.8, 6.9}}</ref>

Aware of the importance of causal structure, [[Roger Penrose]] and others developed what is known as [[Spacetime topology|global geometry]]. In global geometry, the object of study is not one particular solution (or family of solutions) to Einstein's equations. Rather, relations that hold true for all geodesics, such as the [[Raychaudhuri equation]], and additional non-specific assumptions about the nature of matter (usually in the form of [[energy conditions]]) are used to derive general results.<ref>{{Harvnb|Wald|1984|loc=sec. 9.2–9.4}} and {{Harvnb|Hawking|Ellis|1973|loc=ch. 6}}</ref>