https://doi.org/10.1140/epjp/s13360-022-03578-7
Regular Article
Kasner universes in 
gravity
1
Institute of Systems Science, Durban University of Technology, 4000, Durban, South Africa
2
Departamento de Matemáticas, Universidad Católica del Norte, Avda. Angamos 0610, Casilla 1280, Antofagasta, Chile
Received:
3
August
2021
Accepted:
7
December
2022
Published online:
17
December
2022
In the context of the modified higher-order teleparallel 
gravity and specifically in the case of 
theory, we investigate the existence of anisotropic solutions in a Bianchi I spacetime. Invariant 
is defined as 
, in which B is term which relates the Ricciscalar R with the torsion scalar T, 
, and is also a boundary term. We investigate the existence of Kasner and Kasner-like solutions. We find the conditions for the limit of General Relativity, while Kasner-like solutions exist as asymptotic solutions for the field equations. Furthermore, anisotropic exponential solutions are not preferred by the theory. As far as the Kasner universes are concerned, we show that they are always unstable in this fourth-order theory of gravity. Finally, we discuss the condition for the general theory where the Kasner universes are recovered.
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