  We describe the quantum theory of isolated horizons with electromagnetic or
non-Abelian gauge charges in a setting in which both gauge and gravitational
field are quantized. We consider the distorted case, and its spherically
symmetric limit. We show that the gravitational horizon degrees of freedom give
rise to the Bekenstein-Hawking relation, with lower order terms giving some
corrections for small black holes. We also demonstrate that one can include
matter degrees of freedom into the state counting. We show that one can expect
(potentially divergent) contributions proportional to the area, as well as
logarithmic correction proportional to the horizon charge. This is
qualitatively similar to results on matter contributions obtained with other
methods in the literature.
