Chinese Acad Sci, Inst High Energy Phys, Beijing 100039, Peoples R China
; Chinese Acad Sci, Inst Theoret Phys, Beijing 100080, Peoples R China
; CCAST, World Lab, Beijing 100080, Peoples R China
; Max Planck Inst Gravitat Phys, D-14476 Golm, Germany
The Noether-charge and the Hamiltonian realizations for the diff(M) algebra in diffeomorphism-invariant gravitational theories without a cosmological constant in any dimension are studied in a covariant formalism. We analyze how the Hamiltonian functionals form the diff(M) algebra under the Poisson brackets and show how the Noether charges with respect to the diffeomorphism generated by the vector fields and their variations in n-dimensional general relativity form this algebra. The asymptotic behaviors of vector fields generating diffeomorphism of the manifold with boundaries are discussed. It is shown that the "central extension" for a large class of vector fields is always zero on the Killing horizon. We also check whether choosing the vector fields near the horizon may pick up the Virasoro algebra. The conclusion is unfortunately negative in any dimension.