https://doi.org/10.1140/epjp/s13360-022-03278-2
Regular Article
Anisotropic spacetimes in f(T, B) theory IV: Noether symmetry analysis
1
Institute of Systems Science, Durban University of Technology, 4000, Durban, South Africa
2
Instituto de Ciencias Físicas y Matemáticas, Universidad Austral de Chile, 5090000, Valdivia, Chile
Received:
11
May
2022
Accepted:
7
September
2022
Published online:
20
September
2022
The Noether symmetry analysis is applied for the analysis of the field equations in an anisotropic background in f(T, B)-theory. We consider the 
which describes a small deviation from TEGR introduced by the boundary scalar B. For the Bianchi I, Bianchi III and Kantowski–Sachs geometries, there exists a minisuperspace description and Noether’s theorems are applied. We investigate the existence of invariant point transformations. We find that for the Bianchi I spacetime, the gravitational field equations are Liouville integrable for the 
theory. The analytic solution is derived, and the application of Noether’s symmetries to the Wheeler–DeWitt equation of quantum cosmology is discussed.
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© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2022. Springer Nature or its licensor holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
