Is there a formal term for the set of all (geodesic) curves passing through a point?

Question

My context is the spacetime of general relativity. I want to describe the fact that every spacetime event is the intersection of an infinite number of world-lines. I found myself reaching for a term that would identify the set of all geodesics passing through a point on a (pseudo-) Riemann manifold. There is a term pencil in projective geometry that has a similar connotation, but I don't believe it could be made to suit my needs.

Is there a term for the set of all geodesics (or differentiable curves) sharing a common point on a differentiable manifold?

Answer 1

In the context of projective spaces, George A. Jennings's Modern Geometry with Applications gives:

A set of lines is coincident if all the lines intersect at the same point.

So it seems reasonable to use the term coincident set of geodesics to mean a set intersecting at a common point.