Cylindrical Solutions in Modified f(T) Gravity

TL;DR

This paper explores static cylindrically symmetric vacuum solutions in f(T) gravity, deriving new solutions with finite torsion and discussing their relation to known GR solutions, including the cosmological constant's role.

Contribution

It provides explicit solutions in f(T) gravity with finite torsion and connects these to classical GR solutions like Linet-Tian, expanding understanding of cylindrically symmetric spacetimes.

Findings

Derived solutions with finite torsion scalar on the axis

Established relation between f(T) solutions and GR Linet-Tian solutions

Analyzed the impact of cosmological constant in f(T) cylindrically symmetric spacetimes

Abstract

We investigate static cylindrically symmetric vacuum solutions in Weyl coordinates in the framework of f(T) theories of gravity, where T is the torsion scalar. The set of modified Einstein equations is presented and the fourth coming equations are established. Specific physical expressions are assumed for the algebraic function f(T) and solutions are obtained. Moreover, general solution is obtained with finite values of u(r) on the axis r = 0, and this leads to a constant torsion scalar. Also, cosmological constant is introduced and its relation to Linet-Tian solution in GR is commented.