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We investigate a linearized tensor-tensor theory of gravity with torsion anda perturbed torsion wave solution is discovered in background Minkowskispacetime with zero torsion. Furthermore, gauge transformations of anyperturbed tensor field are derived in general background non-Riemanniangeometries. By calculating autoparallel deviations, both longitudinal andtransverse polarizations of the torsion wave are discovered.

Linearized Torsion Waves in a Tensor-Tensor Theory of Gravity