Wave operators, torsion, and Weitzenböck identities

The current article offers a mathematical toolkit for the study of waves propagating on spacetimes with nonvanishing torsion. comprises generalized versions Lichnerowicz–de Rham and Beltrami wave operators, Weitzenböck identity relating them Riemann–Cartan geometries. construction applies to any field belonging matrix representation Lie (super) algebra containing an $$\mathfrak {so} \left( \eta _{+}, _{-} \right) $$ subalgebra. These tools allow us propagation Einstein–Cartan background at different orders in eikonal parameter. It stands strong contrast more traditional approaches that are restricted studying only leading order this kind geometry (“plane waves”). focuses aspects proofs generalizations some results already used physical applications. In particular, subleading analysis proves torsion affects amplitude polarization fields representations. suggest how one may use gravitational multimessenger events as probes spin tensor dark matter.