Noether-charge realization of diffeomorphism algebra

We present the Noether-charge realization of the diffeomorphism invariance of the gravitational theory in the covariant phase space formalism. With the help of the null tetrad well defined on the horizon, it is shown that the central term vanishes for the reduced diffeomorphism algebra on the Killing horizon with respect to a large class of vector fields in the vacuum general relativity.