  Physical process version of the first law of black hole thermodynamics in
Einstein- Maxwell dark matter gravity was derived. The dark matter sector is
mimicked by the additional U(1)-gauge field coupled to the ordinary Maxwell
one. By considering any cross section of the black hole event horizon to the
future of the bifurcation surface, the equilibrium state version of the first
law of black hole mechanics was achieved. The considerations were generalized
to the case of Einstein- Yang-Mills dark matter gravity theory. The main
conclusion is that the influence of dark matter is crucial in the formation
process of black objects. This fact may constitute the explanation of the
recent observations of the enormous mass of the super luminous quasars formed
in a relatively short time after Big Bang. We also pay attention to the compact
binaries thermodynamics, when dark matter sector enters the game.
