Eur. Phys. J. C (2020) 80: 108
https://doi.org/10.1140/epjc/s10052-020-7666-7

Regular Article - Theoretical Physics

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

¹ Department of Astoronomy and Space Sciences, Istanbul University, Beyazit, 34134, Istanbul, Turkey
² Dipartimento di Fisica “E. Pancini”, Università di Napoli “Federico II”, Via Cinthia, 80126, Naples, Italy
³ Istituto Nazionale di Fisica Nucleare (INFN), Sez. di Napoli, Via Cinthia 9, 80126, Naples, Italy
⁴ Laboratory for Theoretical Cosmology, Tomsk State University of Control Systems and Radioelectronics (TUSUR), 634050, Tomsk, Russia
⁵ Department of Physics, Mimar Sinan Fine Arts University, Bomonti, 34380, Istanbul, Turkey
⁶ Institute of Graduate Studies in Sciences, Istanbul University, Beyazit, 34134, Istanbul, Turkey

^* e-mail: ali.nurbaki@ogr.istanbul.edu.tr
^** e-mail: anurbaki@yahoo.com

Received: 30 December 2019
Accepted: 18 January 2020
Published online: 10 February 2020

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.