  Angular momentum and mass-charge inequalities for axisymmetric maximal
time-symmetric initial data in Einstein-Maxwell gravity with dark matter sector
were derived. The dark matter sector is mimicked by another U(1)-gauge field
coupled to the ordinary Maxwell one. We assume that data set with two
asymptotically flat regions is given on smooth simply connected manifold. One
also pays attention to the area momentum charge inequalities for a closed
orientable two-dimensional spacelike surface embedded in the spacetime of the
considered theory. It turned out that the addition of dark matter sector
influences to the great extent on the growth of the black hole masses. This
fact may be responsible for the existence of the recently detected supermassive
objects at relatively short time after Big Bang. The inequalities binding the
charge of the body (black hole) and its size were also investigated. It turns
out that the estimation depends on the coupling constant of the ordinary matter
to the dark matter sector.
