Maximal geodesic

A geodesic $\gamma :I\to M$ is maximal when it has no geodesic extension to a strictly larger interval. Every initial position and velocity determine a unique maximal geodesic through the geodesic equation.

An extendible geodesic is a geodesic segment that can be continued beyond at least one endpoint within the same manifold after retaining an affine parameter. An artificial truncation at a regular event is extendible even when its continuation eventually reaches a singularity.