  Context: The origin of ultra-rapid flares of very high-energy radiation from
active galactic nuclei remains elusive. Magnetospheric processes, occurring in
the close vicinity of the central black hole, could account for these flares.
  Aims: We aim to bridge the gap between simulations and observations by
synthesizing gamma-ray lightcurves in order to characterize the activity of a
black-hole magnetosphere, using kinetic simulations.
  Methods: We perform global axisymmetric two-dimensional general-relativistic
particle-in-cell simulations of a Kerr black-hole magnetosphere. We include a
self-consistent treatment of radiative processes and plasma supply, as well as
a realistic magnetic configuration, with a large-scale equatorial current
sheet. We couple our particle-in-cell code with a ray-tracing algorithm, in
order to produce synthetic lightcurves.
  Results: These simulations show a highly dynamic magnetosphere, as well as
very efficient dissipation of the magnetic energy. An external supply of
magnetic flux is found to maintain the magnetosphere in a dynamic state,
otherwise the magnetosphere settles in a quasi-steady Wald-like configuration.
The dissipated energy is mostly converted to gamma-ray photons. The lightcurves
at low viewing angle (face-on) mainly trace the spark gap activity and exhibit
high variability. On the other hand, no significant variability is found at
high viewing angle (edge-on), where the main contribution comes from the
reconnecting current sheet.
  Conclusions: We observe that black-hole magnetospheres with a current sheet
are characterized by a very high radiative efficiency. The typical amplitude of
the flares in our simulations is lower than what is detected in active galactic
nuclei. Such flares could result from the variation of parameters external to
the black hole
