Axial torsion waves in metric-affine gravity

TL;DR

This paper constructs explicit vacuum solutions in quadratic metric-affine gravity, generalizing pp-waves to include torsion, and explores their potential relation to electromagnetic and neutrino fields.

Contribution

It introduces new exact solutions in metric-affine gravity with axial torsion, extending classical pp-wave spacetimes and analyzing their physical interpretations.

Findings

Solutions include nonvanishing axial torsion in vacuum

Generalization of pp-waves with metric compatibility

Potential link between torsion and electromagnetic fields

Abstract

We construct new explicit vacuum solutions of quadratic metric-affine gravity. The approach of metric-affine gravity in using an independent affine connection produces a theory with 10+64 unknowns, which implies admitting torsion and possible nonmetricity. Our spacetimes are generalisations of classical pp-waves, four-dimensional Lorentzian spacetimes which admit a nonvanishing parallel spinor field. We generalize this definition to metric compatible spacetimes with pp-metric and purely axial torsion. It has been suggested that one can interpret that the axial component of torsion as the Hodge dual of the electromagnetic vector potential. We compare these solutions with our previous results and other solutions of classical models describing the interaction of gravitational and neutrino fields.