  This work deals with intersection points: conjugate points and cut points, of
timelike geodesics emanating from a common initial point in special spacetimes.
The paper contains three results. First, it is shown that radial timelike
geodesics in static spherically symmetric spacetimes are globally maximal (have
no cut points) in adequate domains. Second, in one of ultrastatic spherically
symmetric spacetimes, Morris--Thorne wormhole, it is found which geodesics have
cut points (and these must coincide with conjugate points) and which ones are
globally maximal on their entire segments. This result, concerning all timelike
geodesics of the wormhole, is the core of the work. The third outcome deals
with the astonishing feature of all ultrastatic spacetimes: they provide a
coordinate system which faithfully imitates the dynamical properties of the
inertial reference frame. We precisely formulate these similarities.
