Polarization structure of gravitational waves in extended relativity

TL;DR

This paper investigates the polarization structure of gravitational waves within Extended Relativity, deriving how different polarization components relate to source geometry and affect detector responses.

Contribution

It introduces a unified framework for analyzing gravitational wave polarization in ER, linking theoretical structure to observable signatures in detectors.

Findings

Polarization components are not independent; their relative amplitudes are fixed by source geometry.

Derived the radiation field of a binary in the wave zone using deviation tensor and retarded phase.

Established how detector responses depend on the polarization structure in ER.

Abstract

We analyze the polarization structure of gravitational waves in the framework of Extended Relativity (ER), using the deviation tensor as the fundamental observable quantity. Starting from the point-source solution, we derive the radiation field of a compact binary in the wave zone and express the deviation tensor in a form in which the spacetime dependence is carried entirely by the retarded phase, while the tensorial coefficients depend only on the inclination angle of the source. This representation allows for a unified treatment of detector responses. For interferometric detectors, the signal is governed by the tidal matrix, which depends on second derivatives of the deviation tensor. For pulsar timing arrays (PTAs), the response follows from null geodesic propagation and reduces to boundary terms, so that the observable is determined by the projection $k^\mu k^\nu h_{\mu\nu}$ evaluated at the emission and reception points. A key result is that the polarization components are not independent: the relative amplitudes of tensor, vector, and scalar contributions are fixed by the source geometry. This leads to a constrained family of polarization states and corresponding PTA correlation patterns. The formulation provides a direct connection between the theoretical structure of ER and observable signatures.