Causal Geodesics in Cylindrically Symmetric Vacuum Spacetimes Using Hamilton-Jacobi Formalism

TL;DR

This paper analyzes the properties of cylindrically symmetric vacuum spacetimes, providing complete solutions for geodesics using Hamilton-Jacobi formalism and comparing relativistic and Newtonian cases.

Contribution

It offers the first comprehensive solution for geodesics in these spacetimes using Hamilton-Jacobi formalism and compares relativistic and Newtonian trajectories.

Findings

Complete solutions for time- and light-like geodesics.

Differences between relativistic and Newtonian particle trajectories.

Insights into properties of cylindrically symmetric vacuum spacetimes.

Abstract

Cylindrically symmetric vacuum spacetimes are of immense interest in theoretical physics due to its connection to cosmic strings hypothesized in quantum field theory. In this article, we explore the properties of such spacetime and provide the complete solution to the time- and light-like geodesics in it using Hamilton-Jacobi formalism. In addition, we compare several properties and massive particle trajectories of relativistic cylindrically symmetric vacuum spacetimes to its non-relativistic, Newtonian gravitational counterparts.