Dirac Analysis and Integrability of Geodesic Equations for Cylindrically Symmetric Spacetimes

TL;DR

This paper applies Dirac's constraint analysis to cylindrically symmetric stationary spacetimes, deriving the symplectic structure and integrating geodesic equations, providing solutions for specific spacetime metrics.

Contribution

It introduces a Dirac-based method to analyze geodesic equations in cylindrically symmetric spacetimes, revealing their integrability and explicit solutions.

Findings

Derived the symplectic structure of geodesic equations

Integrated geodesic equations for Lewis, Levi-Civita, and Van Stockum spacetimes

Obtained explicit solutions for these spacetime metrics

Abstract

Dirac's constraint analysis and the symplectic structure of geodesic equations are obtained for the general cylindrically symmetric stationary spacetime. For this metric, using the obtained first order Lagrangian, the geodesic equations of motion are integrated, and found some solutions for Lewis, Levi-Civita, and Van Stockum spacetimes.