Study of cylindrically symmetric solutions in metric f(R) gravity with constant R

TL;DR

This paper investigates cylindrically symmetric solutions in f(R) gravity assuming constant scalar curvature, deriving new metrics and comparing them with general relativity with a cosmological constant.

Contribution

It introduces new solutions for cylindrically symmetric spacetimes in f(R) gravity with constant R, extending previous results and relating them to GR with a cosmological constant.

Findings

Derived metrics for R=constant in f(R) gravity

Found solutions equivalent to known R=0 case

Compared metrics with general relativity with mbda

Abstract

Solutions for cylindrically symmetric spacetimes in f(R) gravity are studied. As a first approach, R=constant is assumed. A solution was found such that it is equivalent to a result given by Azadi et al. for R=0 and a metric was found for R=constant different from zero. Comparison with the case of general relativity with cosmological constant is made and the metric constants are given in terms of \Lambda. Overlap with arXiv:0810.4673 [gr-qc] by A. Azadi, D. Momeni and M. Nouri-Zonoz