Killing Motion of Static Cylindrically Symmetric Spacetimes in the f(R) Gravity

In this study we have studied "Killing Motion of Static Cylindrically Symmetric Spacetimes in f(R) Gravity" by using algebraic and direct integration techniques. This study investigates the Killing motions of static cylindrically symmetric spacetimes with in framework of f(R) gravity, a generalization of Einstein’s General Relativity. We explore the existence of Killing vector fields to understand the symmetries and conserved quantities in such spacetimes. By analysing the modified field equations, we determine the constraints imposed by f(R) gravity on the geometry and dynamics of cylindrically symmetric spacetimes. These contribute to understanding the interplay between symmetry properties and gravitational theories beyond General Relativity. The results have implications for astrophysical and cosmological models influenced by alternative gravity theories. We discussed four cases and found that the dimension of Killing vector fields is either three, four or ten.