Conserved charges of the Kerr black hole revisited

We revisit the Kerr black hole as cast in the Boyer–Lindquist, Kerr–Schild and Weyl canonical coordinates, and calculate its total mass/energy and total angular momentum using linearized gravity along with its background Killing isometries. We argue that the integration of the relevant gravitational flux does not depend on the geometry of the closed and simply connected spatial boundary provided it is also piecewise smooth.