Massive to gauge field reduction and gravitational wave zone information

We show explicitly that massive, Abelian, vector – just like (properly defined) massive tensor – fields limit smoothly to their massless, gauge, versions: they emit only maximal helicity radiation and mediate Coulomb/“special relativistic Newtonian”, forces between their (conserved) sources. Our main motivation, though, is to show that LIGO’s gravitational wave detection probably cannot directly rule out very long-range gravity: Even though the waves were emitted in a strong field regime, their being detected in the weak field wave zone means the above equivalences apply. There remains the – not unlikely – possibility that no strong field generation of radiation in massive models can reproduce the observed ring-down patterns. Separately, the smooth linear limiting behaviors show that the discontinuity lies not in the mass alone, but rather in Abelian versus non-Abelian – Yang-Mills and General Relativity – regimes, whose respective massive versions are known to be non-physical.