Kinetic energy and angular momentum of free particles in a class of rotating cylindrical gravitational waves using the Noether symmetry approach

In this paper, we investigate the kinetic energy and angular momentum of free particles in a class of rotating cylindrical gravitational wave spacetimes, using the Noether symmetry approach. For that purpose, we determine the conserved quantities and subsequently analyze them for the velocities of free particles in the spacetimes, thereby simplifying the relationship between velocities and coordinates. Our analysis demonstrates that arbitrary choices of metric coefficients lead to fluctuations in the velocity of free particles, thereby causing variations in their kinetic energy under the influence of rotating cylindrical gravitational waves. Furthermore, we derive expressions for the angular momentum imparted to free particles by these waves, considering various scenarios for metric coefficients. Interestingly, we observe that the angular momentum of free particles initially experiences an increase over time but eventually starts to decrease after a certain duration.