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.

9 pages, accepted for publication in EPJ C

References in corpus (6)

• Modified teleparallel gravity: inflation without inflaton
• Einstein's Other Gravity and the Acceleration of the Universe
• Conformal transformation in $f(T)$ theories
• Noether Symmetry Approach in $f(T,B)$ teleparallel cosmology
• Noether Symmetry Approach in Gauss-Bonnet Cosmology
• Scalar-Tensor Teleparallel Wormholes by Noether Symmetries

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• 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