Abstract
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 \(f\left( T,B\right) =T+F\left( B\right) \) theory and we determine the criteria where \(f\left( T,B\right) \)-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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