Eight Local Couplings of Gravitational Waves from Unified Field Equations

A gravitational-wave (GW) detector records a linear mixture of local couplings under the assumption that extra polarizations enter geodesic deviation. Vacuum general relativity (GR) admits two transverse-traceless (TT) amplitudes. It remains to determine the largest set of couplings that can sit in that mixture, and whether a tensor-only arm-length result selects GR uniquely. The little group E(2) of a null four-momentum classifies the strain amplitudes p=(p+,p times,p x,p y,p b,p), commonly written h P, which determine the electric tidal tensor along a ray. Geodesic deviation, recorded as differential arm length, therefore contains only those p P that enter that tensor. Lorentz mixing at helicity plus or minus1 supplies a gravito-magnetic (GEM) field that does not enter the tidal tensor. if GEM field is static, that does not propagate as a wave. A time-varying helicity- plus or minus1 current sources a GEM wave that enters the mixture as a coupling, to be isolated by its measured quantity. For a radiation-zone wave that depends only on retarded time, = times d t(p x,p y), and the eight couplings are =(p,). Here we adopt unified field equations on p to clarify the origin of each component of; the measured quantity of each coupling then isolates the polarizations in that mixture, which favors identification of distinct polarizations and model tests.