The study explores the particle dynamics, asymptotic behavior, and flatness in Riemann curvature corresponding to the solutions obtained from the Ricci tensor of cylindrical spacetimes. Since these solutions are non-Minkowskian and are proposed to have curvature in almost all the cases, that is why some cylindrically symmetric static vacuum solutions of Einstein Field Equations have been worked out. We explore the Noether symmetries along with their conservation laws of the corresponding static-spacetime and calculate the equation of motions by taking into account Noether symmetries. We study the dynamics of particle in the form of effective potential, effective force.

该研究探索了与从圆柱时空的Ricci张量获得的解相对应的粒子动力学，渐近行为和Riemann曲率的平坦度。由于这些解决方案是非Minkowskian的，并且被提议在几乎所有情况下都具有曲率，因此正因如此，已经找到了一些爱因斯坦场方程的圆柱对称静态真空解。我们探索Noether对称性及其对应的静态时空守恒律，并通过考虑Noether对称性来计算运动方程。我们以有效势，有效力的形式研究粒子的动力学。