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This work deals with intersection points: conjugate points and cut points, oftimelike geodesics emanating from a common initial point in special spacetimes.The paper contains three results. First, it is shown that radial timelikegeodesics in static spherically symmetric spacetimes are globally maximal (haveno cut points) in adequate domains. Second, in one of ultrastatic sphericallysymmetric spacetimes, Morris--Thorne wormhole, it is found which geodesics havecut points (and these must coincide with conjugate points) and which ones areglobally maximal on their entire segments. This result, concerning all timelikegeodesics of the wormhole, is the core of the work. The third outcome dealswith the astonishing feature of all ultrastatic spacetimes: they provide acoordinate system which faithfully imitates the dynamical properties of theinertial reference frame. We precisely formulate these similarities.

acta physica polonica. b

Globally maximal timelike geodesics in static spherically symmetric  spacetimes: radial geodesics in static spacetimes and arbitrary geodesic  curves in ultrastatic spacetimes