Cylindrical solutions in metric f(R) gravity

TL;DR

This paper explores static cylindrically symmetric vacuum solutions in metric f(R) gravity, deriving exact solutions for various models, including those with constant Ricci scalar, and discusses their relation to known solutions like cosmic strings and Linet-Tian spacetime.

Contribution

It provides explicit exact solutions in metric f(R) gravity for cylindrically symmetric spacetimes, including new solutions with constant Ricci scalar.

Findings

Derived a single equation for vacuum solutions in f(R) gravity.

Found explicit solutions with constant Ricci scalar, including a cosmic string exterior.

Discussed the relation of new solutions to the Linet-Tian solution.

Abstract

We study static cylindrically symmetric vacuum solutions in Weyl coordinates in the context of the metric f(R) theories of gravity. The set of the modified Einstein equations is reduced to a single equation and it is shown how one can construct exact solutions corresponding to different $f(R)$ models. In particular the family of solutions with constant Ricci scalar ($R=R_{0}$) is found explicitly which, as a special case (R=0), includes the exterior spacetime of a cosmic string. Another new solution with constant, non-zero Ricci scalar is obtained and its possible relation to the Linet-Tian solution in general relativity is discussed.