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 $f(R)=f_0{R}^n$, 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.

arXiv comment9 pages, no figures, version accepted for publication in the European Physical Journal C. arXiv admin note: text overlap with arXiv:2109.08938

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