  Interactions between outgoing Hawking particles and ingoing matter are
determined by gravitational forces and Standard Model interactions. In
particular the gravitational interactions are responsible for the unitarity of
the scattering against the horizon, as dictated by the holographic principle,
but the Standard Model interactions also contribute, and understanding their
effects is an important first step towards a complete understanding of the
horizon's dynamics. The relation between in- and outgoing states is described
in terms of an operator algebra. In this contribution, in which earlier results
are rederived and elaborated upon, we first describe the algebra induced on the
horizon by U(1) vector fields and scalar fields, including the case of an
Englert-Brout-Higgs mechanism, and a more careful consideration of the
transverse vector field components. We demonstrate that, unlike classical black
holes, the quantized black hole has on its horizon an imprint of its (recent)
past history, i.e., quantum hair. The relation between in- and outgoing states
depends on this imprint. As a first step towards the inclusion of non-Abelian
interactions, we then compute the effects of magnetic monopoles both in the
in-states and in the out-states. They completely modify, and indeed simplify,
our algebra.
