The role of closed timelike curves in particle motion within Van Stockum space-time: A generalization

TL;DR

This paper investigates particle motion in Van Stockum space-time with closed timelike curves, revealing that only particles with angular momentum can exist near these curves and analyzing their energy and time jump properties.

Contribution

It generalizes the understanding of particle dynamics in Van Stockum space-time by examining angular momentum effects and providing a comprehensive framework for closed timelike and geodesic curves.

Findings

Only particles with non-zero angular momentum exist near CTCs.

Minimum particle energy in closed timelike geodesics is characterized.

Range of backward time jump in CTCs is analyzed.

Abstract

The present work analyses the particle motion in the Van Stockum space-time considering the existence of closed timelike curves. Test particles with or without angular momentum are studied in the present geometry. It is found that only non-zero angular momentum test particles exist in the neighborhood of closed timelike curves. The minimum particle energy and the range of backward time jump in closed timelike geodesics are studied within a Cauchy horizon. Finally, a general prescription for CTC and CTG has been presented with appropriate examples.