Noether Symmetries and Conservation Laws in Static Cylindrically Symmetric Spacetimes via Rif Tree Approach

A new approach is adopted to completely classify the Lagrangian associated with static cylindrically symmetric spacetime metric via Noether symmetries. The determining equations representing symmetries are analyzed using a Maple algorithm that imposes different conditions on coefficients under which spacetimes admit of dimensions. These used solve equations, giving explicit form vector fields obtained symmetry generators in Noether’s theorem find expressions for corresponding conservation laws. singularity metrics discussed by finding their Kretschmann scalar.