Anisotropic spacetimes in $f(T,B)$ theory III: LRS Bianchi III Universe

We study the asymptotic dynamics of $f(T,B)$-theory in an anisotropic Bianchi III background geometry. We show that an attractor always exists for the field equations, which depends on a free parameter provided by the specific $f(T,B)$ functional form. The attractor is an accelerated spatially flat FLRW or non-accelerated LRS Bianchi III geometry. Consequently, the $f(T,B)$-theory provides a spatially flat and isotropic accelerated Universe.