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Anisotropic spacetimes in f(T, B) theory I: Bianchi I universe

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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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  1. Institute of Systems Science, Durban University of Technology, Durban, 4000, South Africa

    Andronikos Paliathanasis

  2. Instituto de Ciencias Físicas y Matemáticas, Universidad Austral de Chile, 5090000, Valdivia, Chile

    Andronikos Paliathanasis

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Paliathanasis, A. Anisotropic spacetimes in f(T, B) theory I: Bianchi I universe. Eur. Phys. J. Plus 137, 887 (2022). https://doi.org/10.1140/epjp/s13360-022-03082-y

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