Noether gauge symmetries of geodesic motion in stationary and nonstatic Gödel-type spacetimes

In this study, we obtain Noether gauge symmetries of geodesic motion for geodesic Lagrangian of stationary and nonstatic Gödel-type spacetimes, and find the first integrals of corresponding spacetimes to derive a complete characterization of the geodesic motion. Using the obtained expressions for [Formula: see text] of each spacetimes, we explicitly integrate the geodesic equations of motion for the corresponding stationary and nonstatic Gödel-type spacetimes.

DIRAC ANALYSIS AND INTEGRABILITY OF GEODESIC EQUATIONS FOR CYLINDRICALLY SYMMETRIC SPACETIMES

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.