Polarization structure of gravitational waves in extended relativity

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 $k^μk^νh_{μν}$ 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.