Relativistic Shedding: A Kinematic Threshold for Emission into Weakly Coupled Eigenmodes

We define _Relativistic Shedding_ (RS) as a kinematic threshold phenomenon: a steadily moving relativistic source can radiate into any _propagating_ eigenmode of the coupled field–environment system whose phase velocity (along the source direction) is below the source velocity. Cherenkov radiation is the electromagnetic special case in a dielectric. RS generalizes the same phase-velocity/synchronism criterion to _weakly coupled_ eigenmodes, including hidden-sector states accessed through portal interactions. This paper provides a self-contained foundation for RS intended to remain stable under future model, laboratory, and cosmological refinements. We present: (i) a concise, textbook-level definition; (ii) threshold criteria in both the bulk-medium language (\({\beta n_{eff}} > 1\)) and the guided/periodic-structure language (synchronism \(\omega = {k_{z}v}\)); (iii) a model-independent radiation formula in linear-response (retarded Green-function / spectral-density) form that makes the origin of the step-like turn-on explicit; and (iv) a worked example for a kinetically mixed massive vector (“dark photon”), including the in-medium effective mixing factor. We also state a minimal, falsifier-rich laboratory logic: RS predicts a reversible on/off contrast under ABAB threshold bracketing, rather than a claim about absolute rates. Implementations and cosmological applications are deferred to companion studies.