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

TL;DR

This paper derives new static cylindrically symmetric solutions in General Relativity with unconventional equations of state by applying Noether symmetry methods to $f(R)$ gravity, revealing unknown EoS parameter values.

Contribution

It introduces novel exact solutions in GR for specific EoS parameter values using Noether symmetry analysis, expanding the solution space for cylindrically symmetric spacetimes.

Findings

New exact solutions for non-dust matter in GR

Identification of unknown EoS parameter values

Application of Noether symmetry to $f(R)$ gravity

Abstract

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 $f(R)=f_0 R$ 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.