Spherical and cylindrical solutions in f(T) gravity by Noether symmetry approach

Abstract

We find exact solutions for f (T ) teleparallel gravity for the cases of spherically and cylindrically symmetric tetrads. The adopted method is based on the search for Noether symmetries of point-like Lagrangians defined in Jordan and Einstein frames. Constants of motion are used to reduce the dynamical system. We first consider the Lagrangian defined in the Jordan frame for a spherically symmetric tetrad and, by the help of two constants of motion, we eliminate a tetrad potential and integrate the other. The more complicated structure in the Einstein frame is also overcome by the same method. After that we obtain the Jordan frame Lagrangian for a general cylindrically symmetric tetrad. Following the same procedure adopted in the spherically symmetric case, we again obtain the tetrad potentials and then the exact solutions.

FLRW Cosmological Models with Dynamic Cosmological Term in Modified Gravity

“…At present, our model exhibits quintessence with ω > −1. Thus, our derived model is in keeping with observations [75][76][77].…”

Teleparallel Gravity: From Theory to Cosmology

“…In Ref. [827], the authors used the Noether's symmetry approach to find solutions for f (T ) gravity but they are just written implicitly and not in an exact form for the metric coefficients. In Refs.…”

Noether symmetry approach in Eddington-inspired Born–Infeld gravity

“…Moreover, the existence of Noether symetries plays crucial roles when studying quantum cosmology [39]. The Noether symmetry approach has been employed to various cosmological scenarios so far including the f (T ) gravity [40], the f (R) gravity [41], the alpha-attractors [42], spherical and cylindrical solutions in f (T ) gravity [43], f (G) gravity [44], non-local curvature and Gauss-Bonnet cosmologies [45], and others cosmological scenarios, e.g. [46][47][48][49][50][51][52][53][54][55].…”