  Galactic black hole coronae are composed of a hot, magnetized plasma. The
spectral energy distribution produced in this component of X-ray binaries can
be strongly affected by different interactions between locally injected
relativistic particles and the matter, radiation and magnetic fields in the
source. We study the non-thermal processes driven by the injection of
relativistic particles into a strongly magnetized corona around an accreting
black hole. We compute in a self-consistent way the effects of relativistic
bremsstrahlung, inverse Compton scattering, synchrotron radiation, and the
pair-production/annihilation of leptons, as well as hadronic interactions. Our
goal is to determine the non-thermal broadband radiative output of the corona.
The set of coupled kinetic equations for electrons, positrons, protons, and
photons are solved and the resulting particle distributions are computed
self-consistently. The spectral energy distributions of transient events in
X-ray binaries are calculated, as well as the neutrino production. We show that
the application to Cygnus X-1 of our model of non-thermal emission from a
magnetized corona yields a good fit to the observational data. Finally, we show
that the accumulated signal produced by neutrino bursts in black hole coronae
might be detectable for sources within a few kpc on timescales of years. Our
work leads to predictions for non-thermal photon and neutrino emission
generated around accreting black holes, that can be tested by the new
generation of very high energy gamma-ray and neutrino instruments.
