Cylindrically symmetric and plane-symmetric solutions in f(R) theory via Noether symmetries

Abstract

The f(R) theory is considered for static cylindrically symmetric and plane-symmetric spacetimes. In order to find solutions to the field equations of these models, the Noether symmetry method is used. First, we examine the GR case for cylindrically symmetrical space-time with the w=-1 dark energy state. Then, with the assumption of f(R) = f_0R^n, cases with matter and non-matter are examined and general solutions are determined for both space-times. Thus, it is shown that inclusive new solutions are obtained, considering the Noether symmetric conditions. In addition, the GR limit for each cases are examined.