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.

arXiv comment9 pages, accepted for publication in EPJ C

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• Stellar Structures in $f(\mathcal{G})$ Gravity Admitting Noether Symmetries
• Transit cosmological models in Myrzakulov F(R,T) gravity theory
• A Complete Cosmological Scenario in Teleparallel Gravity
• Static spherically symmetric perfect fluid solutions in teleparallel F(T) gravity
• Myrzakulov $F(T,Q)$ gravity: cosmological implications and constraints
• Noether Symmetry Approach in Eddington-inspired Born-Infeld gravity
• Cylindrically symmetric and plane-symmetric solutions in $f(R)$ theory via Noether symmetries
• Noether symmetry approach in non-minimal derivative coupling gravity
• Noether gauge symmetry approach applying for the non-minimally coupled gravity to the Maxwell field