Cylindrically Symmetric Solutions in $f(R,T)$ Gravity

TL;DR

This paper derives exact cylindrically symmetric solutions in $f(R,T)$ gravity, including models resembling cosmic strings and electromagnetic fields, expanding understanding of such spacetimes in modified gravity theories.

Contribution

It presents new exact solutions in $f(R,T)$ gravity for different models, including cosmic string and electromagnetic field configurations.

Findings

Solutions correspond to cosmic string exterior metrics.

Additional solutions include non-null electromagnetic fields.

Energy densities are explicitly evaluated.

Abstract

The main purpose of this paper is to investigate the exact solutions of cylindrically symmetric spacetime in the context of $f(R,T)$ gravity [1], where $f(R,T)$ is an arbitrary function of Ricci scalar $R$ and trace of the energy momentum tensor $T$. We explore the exact solutions for two different classes of $f(R,T)$ models. The first class $f(R,T)=R+2f(T)$ yields a solution which corresponds to an exterior metric of cosmic string while the second class $f(R,T)=f_1(R)+f_2(T)$ provides an additional solution representing a non-null electromagnetic field. The energy densities and corresponding functions for $f(R,T)$ models are evaluated in each case.