https://doi.org/10.1140/epjc/s10052-023-11964-3
Regular Article - Theoretical Physics
Anisotropic solutions in symmetric teleparallel 
-theory: Kantowski–Sachs and Bianchi III LRS cosmologies
1
Center for Theoretical Physics, College of Physics, Sichuan University, 610065, Chengdu, China
2
Nuclear and Particle Physics Section, Physics Department, University of Athens, 15771, Athens, Greece
3
Institute of Systems Science, Durban University of Technology, 4000, Durban, South Africa
4
Departamento de Matemáticas, Universidad Católica del Norte, Avda. Angamos 0610, Casilla 1280, Antofagasta, Chile
a nsdimakis@scu.edu.cn, nsdimakis@gmail.com
Received:
14
August
2023
Accepted:
25
August
2023
Published online:
8
September
2023
We investigate the existence of anisotropic self-similar exact solutions in symmetric teleparallel -theory. For the background geometry we consider the Kantowski–Sachs and the Locally Rotationally Symmetric Bianchi type III geometries. These two anisotropic spacetimes are of special interest because in the limit of isotropy they are related to the closed and open Friedmann–Lemaître–Robertson–Walker cosmologies respectively. For each spacetime there exist two distinct families of flat, symmetric connections, which share the symmetries of the spacetime. We present the field equations, and from them, we determine the functional form of the Lagrangian which yields self-similar solutions. We initially consider the vacuum case and subsequently we introduce a matter source in terms of a perfect fluid. Last but not least, we report some self-similar solutions corresponding to static spherically symmetric spacetimes.
© The Author(s) 2023
Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.
