New gravitational wave polarization modes in the torsionless spacetime

TL;DR

This work analyzes gravitational-wave polarization in a torsionless Palatini gravity framework with non-metricity. It develops a gauge-invariant perturbation approach and derives a modified equation of motion for free particles, showing that non-metricity induces two new shear polarization modes, P7 and P8, in addition to the standard tensor, vector, and scalar modes. Through a concrete example, the authors find that vector and scalar modes can acquire mass via m^{2} = \alpha/\beta, with detectable shear modes arising for particles carrying hypermomentum while ordinary matter may only exhibit the conventional tensor modes. The results provide a pathway to test spacetime geometry using gravitational-wave detectors and to map theory parameters to observable polarization signatures, potentially revealing non-Riemannian geometric effects in gravity.

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.

Figures (3)

• Figure 1: Six polarization modes of gravitational waves Eardley. The gravitational waves propagate in the $+z$ direction. The solid line represents the shape of the test particle array—initially spherical—depicting the motion of particles relative to the central particle of the sphere when the wave phase is $\frac{\pi}{2}$. The dotted line illustrates the shape of the array at a phase of $\frac{3}{2}\pi$. No relative motion occurs between test particles along the third axis, which is not shown in the figure.
• Figure 2: The two new shear modes. The gravitational waves in the figure propagate in the $+z$ direction. In the shear-$x$ and shear-$y$ modes, the periodic tangential motion of a test particle array occurs along the $x$ and $y$ directions, respectively. In addition, the amplitude of this motion increases with the relative distance in the $z$-direction between the test particles. The solid and dashed lines represent the cases where the phases are labeled as $\frac{\pi}{2}$ and $\frac{3}{2}\pi$, respectively.
• Figure 3: Schematic diagram illustrating the relative motion of test particles over one period under shear-mode gravitational waves.