The story
From the physics concept of "at infinity" or "far", where fields are small, and the math concept of null set. Ironically, a null infinity may be neither far nor a null set.
Etymology from Wiktionary, CC BY-SA 4.0.
null infinity
Today it means: In a closed space-time, especially for an Einstein cylinder, null infinity for a given point is the limit of convergence of the light cone most distant from the given point. That is, it is the limit of a set of points that each have a time-like separation from every point that has a space-like separation from the given point. Full definition →