  We analyze possible local extensions of the Poincar\'e symmetry in light-cone
gravity in four dimensions. We use a formalism where we represent the algebra
on the two field degrees of freedom, one with helicity $2$ and the other with
helicity $-2$. The representation is non-linearly realized and one of the
light-cone momenta is the Hamiltonian, which is hence a non-linear generator of
the algebra. We find that this can be locally realized and the Poincar\'e
algebra extended to the BMS symmetry without any reference to asymptotic
limits.
