  The existence of a Killing symmetry in a gauge theory is equivalent to the
addition of extra Hamiltonian constraints in its phase space formulation, which
imply restrictions both on the Dirac observables (the gauge invariant physical
degrees of freedom) and on the gauge freedom.
  When there is a time-like Killing vector field only pure gauge
electromagnetic fields survive in Maxwell theory in Minkowski space-time ,
while in ADM canonical gravity in asymptotically Minkowskian space-times only
inertial effects without gravitational waves survive.
