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Distorted Torsion Tensor, Teleparallelism and Spin 2 Field Equations

A notion of distorted torsion tensor was introduced by Okubo, in the establishment of the Nijenhuis-Bianchi identity and of BRST-like operators. These quantities are constructed with the help of the Nijenhuis tensor, which in turn is defined in terms of a (1,1) tensor $S^λ_μ$. This tensor enters the construction of the distorted torsion tensor. We use this tensor to extend the teleparallel equivalent of general relativity (TEGR) into a theory defined by the tetrad fields and by the tensor $S^λ_μ$. The ordinary TEGR is recovered if $S^λ_μ=δ^λ_μ$. We consider the flat space-time formulation of the theory, in terms of $S^λ_μ$ only, and show that this tensor satisfies the wave equation for massless spin 2 fields.