Eight Local Couplings of Gravitational Waves from Unified Field Equations
Abstract
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×,px,py,pb,pℓ), commonly written hP, which determine the electric tidal tensor along a ray. Geodesic deviation, recorded as differential arm length, therefore contains only those pP that enter that tensor. Lorentz mixing at helicity ±1 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-±1 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, betag⊥=k̂×∂t(px,py), and the eight couplings are Pvec=(p,betag⊥). Here we adopt unified field equations on p to clarify the origin of each component of Pvec; the measured quantity of each coupling then isolates the polarizations in that mixture, which favors identification of distinct polarizations and model tests.
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BibTeX
@misc{jin2026eight,
title = {{Eight Local Couplings of Gravitational Waves from Unified Field Equations}},
author = {Hong-Bo Jin and Yue-Liang Wu},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.03979},
eprint = {2609.03979},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.03979},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Eight Local Couplings of Gravitational Waves from Unified Field Equations
AU - Hong-Bo Jin
AU - Yue-Liang Wu
PY - 2026
DA - 2026/09/03
PB - arXiv
DO - 10.48550/arxiv.2609.03979
UR - https://arxiv.org/abs/2609.03979
AB - 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_×,p_x,p_y,p_b,p_ℓ), 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 ±1 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-±1 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, betag_⊥=k̂×∂_t(p_x,p_y), and the eight couplings are Pvec=(p,betag_⊥). Here we adopt unified field equations on p to clarify the origin of each component of Pvec; the measured quantity of each coupling then isolates the polarizations in that mixture, which favors identification of distinct polarizations and model tests.
ER -