Conserved charges in general relativity

We present a precise definition of a conserved quantity from an arbitrary covariantly conserved current available in a general curved spacetime. This definition enables us to define energy and momentum for matter by the volume integral. As a result we can compute charges of well-known black holes just as an electric charge of an electron in electromagnetism by the volume integration of a delta function singularity. As a byproduct we show that the definition leads to a correction to the known mass formula of a compact star in the Oppenheimer-Volkoff equation. We finally comment on a definition of generators associated with a vector field on a general curved manifold.