https://doi.org/10.1140/epjp/s13360-022-03082-y
Regular Article
Anisotropic spacetimes in f(T, B) theory I: Bianchi I universe
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:
17
July
2022
Published online:
4
August
2022
That is the first part of a series of studies on analyzing the higher-order teleparallel theory of gravity known as the f(T, B)-theory. This work attempts to understand how the anisotropic spacetimes are involved in the f(T, B)-theory. In this work, we review the previous analysis of f(T, B)-gravity, and we investigate the global dynamics in the case of a locally rotational Bianchi I background geometry. We focus in the case of 
theory and we determine the criteria where 
-theory solves the homogeneity problem. Finally, the integrability properties for the field equations are investigated by applying the Painlevé analysis. The analytic solution is expressed by a right Painlevé expansion.
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