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

## TL;DR

This paper investigates the properties of timelike geodesics in static and ultrastatic spherically symmetric spacetimes, identifying conditions for maximality and conjugate points, with applications to wormholes and inertial frame analogies.

## Contribution

It establishes conditions under which radial geodesics are globally maximal and characterizes cut points in ultrastatic wormholes, revealing unique properties of ultrastatic spacetimes.

## Key findings

- Radial timelike geodesics in static spherically symmetric spacetimes are globally maximal.
- Identified which geodesics in Morris–Thorne wormholes have cut points.
- Ultrastatic spacetimes mimic inertial frame properties with precise coordinate formulations.

## Abstract

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.