  We rigorously prove, for the first time, that the non-hydrodynamic sector is
gapless in any relativistic kinetic theory whose scattering cross-section
decays to zero at large energies. In fact, if particles with very high energy
(compared to the temperature) are free streaming, we can use them to build hot
non-hydrodynamic waves, which live longer than any hydrodynamic wave. Since
many standard cross-sections in quantum field theory vanish at high energies,
the existence of these non-thermal long-lived waves is a rather general feature
of relativistic systems.
