  We derive formulas for variations of mass, angular momentum and canonical
energy in Einstein (n-2)-gauge form field theory by means of the ADM formalism.
Considering the initial data for the manifold with an interior boundary which
has the topology of (n-2)-sphere we obtained the generalized first law of black
hole thermodynamics. Supposing that a black hole evevt horizon comprisesw a
bifurcation Killing horizon with a bifurcate surface we find that the solution
is static in the exterior world, when the Killing timelike vector field is
normal to the horizon and has vanishing electric or magnetic fields on static
slices.
