Gravitational wave polarization modes and the kinematical tensors in general relativity and beyond

TL;DR

This paper explores the relationships between kinematical tensors and gravitational wave polarization modes across various metric theories, offering new insights into their interpretation and potential phenomenological implications.

Contribution

It establishes exact and linearized relations between kinematical tensors and polarization modes in general and beyond general relativity, enhancing understanding of gravitational wave phenomenology.

Findings

Transverse shear relates to tensor polarization mode.

Expansion correlates with scalar and longitudinal modes.

Kinematical tensors provide new interpretative tools for gravitational wave analysis.

Abstract

Relations between the kinematical tensors (the expansion, the shear, and the vorticity) and the polarization modes of gravitational waves are studied within the context of metric theories of gravity by considering freely falling test particles. After analyzing exact relations, we consider slowly moving particles under the influence of a weak gravitational field. Linearized plane waves of theories representative of those determined by a general second-order Lagrangian, including General Relativity, are shown to exemplify the following interconnections: between the transverse components of the shear and the transverse tensor polarization mode; between the expansion, and both the transverse scalar and the longitudinal polarization modes; and between the longitudinal-transverse components of both the shear and the vorticity, and the vector polarization mode. These relations, from the theoretical point of view, offer a novel insight into the interpretation of the polarization modes in terms of the kinematical tensors. Additionally, the inclusion of the kinematical tensors in the study of gravitational waves might provide a new outlook on their phenomenology.