A new study proposes an extension to the number of local couplings a gravitational wave could exhibit, moving from the two predicted by General Relativity to a total of eight. This proposal arises from considering additional polarizations that might influence geodesic deviation, the effect measured by gravitational wave detectors. Vacuum General Relativity predicts only two transverse-traceless (TT) polarization amplitudes, but this research aims to determine the broadest set of couplings that could be present in the detected mixture.

The classification of strain amplitudes is based on the little group E(2) of a null four-momentum, which describes the six standard polarizations: p+, p×, px, py, pb, and pℓ. However, geodesic deviation, recorded as the differential arm length of a detector, is only sensitive to those polarizations that directly affect the electric tidal tensor along the ray. The study points out that Lorentz mixing at helicity ±1 introduces a gravito-magnetic (GEM) field which, if static, does not propagate as a wave and thus does not enter the tidal tensor.

Nevertheless, a time-varying helicity-±1 current can source a GEM wave that would couple into the detected mixture. This GEM wave, which in the radiation zone depends only on retarded time, is represented as a vector transverse to the wave vector. By combining the six standard polarizations with the two components of this transverse gravito-magnetic field (βg⊥), the eight proposed couplings are obtained. Adopting unified field equations for these polarizations clarifies the origin of each component, facilitating the identification of distinct polarizations and more precise model tests.

This expanded framework could be crucial for analyzing gravitational wave detector data, enabling the search for deviations from General Relativity. By isolating the measured quantities of each coupling, scientists could identify new polarizations not accounted for in the standard model of gravity, opening the door to exploring unified field theories and gaining a deeper understanding of the nature of gravity and spacetime.