Wave Operators, Torsion, and Weitzenb\"ock Identities
Abstract
We offer a mathematical toolkit for the study of waves propagating on a background manifold with nonvanishing torsion. Examples include electromagnetic and gravitational waves on a spacetime with torsion. The toolkit comprises generalized versions of the Lichnerowicz-de Rham and the Beltrami wave operators, and the Weitzenb\"ock identity relating them on Riemann-Cartan geometries. The construction applies to any field belonging to a matrix representation of a Lie (super) algebra containing an subalgebra. Using these tools, we analyze the propagation of different massless waves in the eikonal (geometric optics) limit in a model-independent way and find that they all must propagate at the speed of light along null torsionless geodesics, in full agreement with the multimessenger observation GW170817/GRB170817A. We also discuss how gravitational waves could be used as a probe to test for torsion.
Cite
@article{arxiv.1903.04712,
title = {Wave Operators, Torsion, and Weitzenb\"ock Identities},
author = {José Barrientos and Fernando Izaurieta and Eduardo Rodríguez and Omar Valdivia},
journal= {arXiv preprint arXiv:1903.04712},
year = {2020}
}
Comments
22 pages, 2 figures