  Low-luminosity supermassive and stellar-mass black holes (BHs) may be
embedded in a collisionless and highly magnetized plasma. They show non-thermal
flares indicative of efficient dissipative processes in the vicinity of the BH.
During NIR flares from the supermassive BH Sagittarius A* (Sgr A*), GRAVITY
detected circular motion and polarization evolution which suggest the presence
of transient synchrotron-emitting hot spots moving around the BH. We study 3D
reconnecting current layers in the magnetosphere of spinning BHs to determine
whether plasma-loaded flux ropes formed near the event horizon could reproduce
the hot spot observations and help constraining the BH spin. We perform global
3D particle-in-cell simulations in Kerr spacetime of a pair plasma embedded in
a strong large-scale magnetic field originating in a disk in prograde Keplerian
rotation. A cone-shaped current layer develops which surrounds the twisted open
magnetic field lines threading the event horizon. Magnetic field lines coupling
the disk to the BH inflate and reconnect a few gravitational radii above the
disk. Particles accelerate and accumulate in a few rotating macroscopic flux
ropes. Once flux ropes detach, they propagate in the current layer following
what appears as a rapidly opening spiral when seen face-on. A single flux rope
carries enough relativistic particles to emit synchrotron radiation at levels
suitable to reproduce the flares' peak-luminosity of Sgr A* but it quickly
fades away as it flows away. Our kinematic analysis of flux ropes' motion
favors a BH spin of 0.65 to 0.8 for Sgr A*. The flares' duration require that
the underlying magnetic loop seeded in the disk mid-plane has a finite lifetime
and azimuthal extent. In this scenario, the hot spot corresponds to a spinning
arc along which multiple reconnection sites power the net emission as flux
ropes episodically detach.
