New gravitational wave polarization modes in the torsionless spacetime

Abstract In this study, we investigate the polarization properties of gravitational waves within a torsionless spacetime framework, as described by the Palatini formalism. Our analysis uncovers the presence of two novel polarization modes, referred to as shear modes, which extend beyond the traditional set of six modes in a four-dimensional Riemannian spacetime. These shear modes, uniquely driven by vector degrees of freedom associated with non-metricity, are classified as vector modes, and their detection provides a unique opportunity to explore the fundamental structure of spacetime and to test gravity theories. These modes extend the standard gravitational wave polarization paradigm and provide novel observational signatures for gravitational wave detectors.