New static cylindrical symmetric solutions in GR for unfamiliar EoS parameter values via Noether symmetry

The solutions for the field equations of f(R) gravity are investigated in static cylindrically symmetric space-time. Conserved quantities of the system, as well as unknown functions, can be determined with the help of the Noether symmetry method. In this article, some unknown values of the equations of state parameter (EoS) have emerged as a result of the constraints obtained by analyzing the Noether symmetry equations for the $f\left(R\right)={f}_{0}R$ case. Consequently, several new exact solutions have been found for cases of General Relativity in static cylindrically symmetrical space-time for the non-dust matter.